Seminar Calendar
for events the year of Saturday, July 21, 2012.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      June 2012              July 2012             August 2012
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2    1  2  3  4  5  6  7             1  2  3  4
3  4  5  6  7  8  9    8  9 10 11 12 13 14    5  6  7  8  9 10 11
10 11 12 13 14 15 16   15 16 17 18 19 20 21   12 13 14 15 16 17 18
17 18 19 20 21 22 23   22 23 24 25 26 27 28   19 20 21 22 23 24 25
24 25 26 27 28 29 30   29 30 31               26 27 28 29 30 31



Thursday, January 12, 2012

Mathematics Colloquium - Special Lecture 2011-12
2:00 pm   in 345 Altgeld Hall,  Thursday, January 12, 2012
 Del Edit Copy
Submitted by kapovich.
 Robert Erhardt (University of North Carolina, Chapel Hill)Approximate Bayesian Computing for Spatial ExtremesAbstract: Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian approaches. In this paper we present a Bayesian approach through the use of approximate Bayesian computing. This circumvents the need for a joint likelihood function by instead relying on simulations from the (unavailable) likelihood. This method is compared with an alternative approach based on the composite likelihood. When estimating the spatial dependence of extremes, we demonstrate that approximate Bayesian computing can provide estimates with a lower mean square error than the composite likelihood approach, though at an appreciably higher computational cost. We also illustrate the performance of the method with an application to US temperature data to estimate the risk of crop loss due to an unlikely freeze event.

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Thursday, January 12, 2012
 Del Edit Copy
Submitted by kapovich.
 Jianfeng Lu (Courant Institute of Mathematical Sciences, New York University)Efficient algorithm for electronic structure calculationsAbstract: Electronic structure theories, in particular Kohn-Sham density functional theory, are widely used in computational chemistry and material sciences nowadays. The computational cost using conventional algorithms is however expensive which limits the application to relative small systems. This calls for development of efficient algorithms to extend the first principle calculations to larger system. In this talk, we will discuss some recent progress in efficient algorithms for Kohn-Sham density functional theory. We will focus on the choice of accurate and efficient discretization for Kohn-Sham density functional theory.

Tuesday, January 17, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, January 17, 2012
 Del Edit Copy
Submitted by jathreya.
 Bill Mance (Ohio State)Explicit constructions of $\mu$-normal numbersAbstract: While there are examples of normal numbers with respect to the b-ary expansions and continued fraction expansion, it has been an open problem to construct normal numbers with respect to many other series expansions. In joint work with Manfred Madritsch we obtain a result that admits explicit constructions of numbers normal with respect to the continued fraction expansion, Luroth series expansion, b-ary expansions, and others.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, January 17, 2012
 Del Edit Copy
Submitted by tzirakis.
 Xuwen Chen (University of Maryland)The Rigorous Derivation of the 2d Cubic NLS with Anisotropic Switchable Quadratic TrapsAbstract: In this talk, we will explain how the nonlinear Schroedinger equations arises from an experimentally observed phenomenon called Bose-Einstein condensation. We will also present a rigorous derivation of the 2d cubic nonlinear Schroedinger equation with anisotropic switchable quadratic traps from a N-body linear Schroedinger equation.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, January 17, 2012
 Del Edit Copy
Submitted by phierony.
 Michael Tychonievich (Ohio State University)Metric Properties of Sets Definable in the Expansion of the Real Field by a Logarithmic SpiralAbstract: We discuss some metric properties of sets definable in certain expansions of the real field, including expansions of the real field by logarithmic spirals. For example, in these structures each bounded definable curve has finite length if and only if the dimension of its frontier is 0.

Mathematics Colloquium - Special Lecture 2011-12
2:00 pm   in 345 Altgeld Hall,  Tuesday, January 17, 2012
 Del Edit Copy
Submitted by kapovich.
 Yiqing Chen (University of Liverpool)Interplay of Dependent Insurance and Financial RisksAbstract: Consider a discrete-time insurance risk model in which the surplus process incorporates both insurance and financial risks. I will look into the stochastic structure of this surplus process and analyze the interplay of the two types of risks. A brief review of extreme value theory in the actuarial context will be included. This talk is based on my recent paper Chen (2011, Journal of Applied Probability).

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Tuesday, January 17, 2012
 Del Edit Copy
Submitted by kapovich.
 David Treumann (Northwestern University)Mirror symmetry and constructible sheavesAbstract: I will give an introduction to the "microlocal" theory of constructible sheaves in the sense of Kashiwara and Schapira, and discuss some recent applications of this theory to Kontsevich's homological mirror symmetry (HMS) conjectures. HMS seeks to relate symplectic geometric objects (such as Lagrangian submanifolds) attached to a symplectic manifold X to complex geometric objects (such as holomorphic vector bundles) attached to a complex manifold Y. The symplectic objects can be described in microlocal terms when X is a cotangent bundle; the cotangent bundle of a compact torus is especially relevant for mirror symmetry. I will discuss the "coherent-constructible correspondence" which matches these objects to coherent sheaves on toric varieties, and an extension of this correspondence to hypersurfaces.

Wednesday, January 18, 2012

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Wednesday, January 18, 2012
 Del Edit Copy
Submitted by kapovich.
 Lindsay Betsy Stovall (UCLA)Counteracting flatness with affine arclength measureAbstract: There are many operators in harmonic analysis for which the curvature of some underlying manifold plays a significant role. We will discuss recent efforts to establish uniform estimates for such operators by compensating for degeneracies of curvature with an appropriate measure. We will focus on the case when the underlying manifolds are polynomial curves.

Thursday, January 19, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, January 19, 2012
 Del Edit Copy
Submitted by ford.
 Kevin Ford (UIUC Math)Values of Euler's function not divisible by a given prime, and the distribution of Euler-Kronecker constants for cyclotomic fieldsAbstract: For a give prime $q>2$, we investigate the first and second order terms in the asymptotic series for the counting function of $n$ with $q\nmid \phi(n)$. Part of the analysis involves the Euler-Kronecker constant $EK(q)$ for the cyclotomic field $Q(e^{2 \pi i/q})$. One of our theorems gives a (conditional on the prime $k$-tuples conjecture) disproof of conjectures of Ihara concerning the distribution of $EK(q)$. The distribution of primes in the arithmetic progression $1\mod q$ plays a central role in the results. This is joint work with Florian Luca and Pieter Moree.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, January 19, 2012
 Del Edit Copy
Submitted by kapovich.
 Organizational meeting

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, January 19, 2012
 Del Edit Copy
Submitted by aimo.
 Atul Dixit (UIUC Math)Convexity of quotients of theta functionsAbstract: For fixed $u$ and $v$ such that $0 \leq u < v < 1/2$, the monotonicity of the quotients of Jacobi theta functions, namely, $\theta_{j}(u|i\pi t)/\theta_{j}(v|i\pi t)$, $j=1, 2, 3, 4$, on $0 < t < \infty$ has been established in the previous works of A.Yu. Solynin, K. Schiefermayr, and Solynin and the author. In the present paper, we show that the quotients $\theta_{2}(u|i\pi t)/\theta_{2}(v|i\pi t)$ and $\theta_{3}(u|i\pi t)/\theta_{3}(v|i\pi t)$ are convex on $0 < t < \infty$. This is joint work with Arindam Roy and Alexandru Zaharescu.

Mathematics Colloquium - Special Lecture 2011-12
2:00 pm   in 345 Altgeld Hall,  Thursday, January 19, 2012
 Del Edit Copy
Submitted by kapovich.
 Runhuan Feng (University of Wisconsin -- Milwaukee)Modeling Investment Guarantees: From Asian option To Titanic optionAbstract: Over the past three decades, the challenge of pricing exotic options such as Asian option in the financial market has inspired theorists and practitioners to pursue innovative techniques. Among many technological breakthroughs on this subject, the work by Marc Yor and co-authors has led to the study of exponential functional of geometric Brownian motion and its integral. Around the same time the insurance market has also experienced dramatic shift from traditional life products to investment-combined products. In order to compete with mutual funds, nearly all major variable annuity writers offer various forms of investment guarantees, nicknamed by some as Titanic options. Although there is no apparent resemblance in the payoffs of Titanic option and Asian option, we found that the analysis on the integral of geometric Brownian motion can be extended to determine risk measures for variable annuity guarantees, which were only known previously by Monte Carlo simulations. In this work, we present for the first time in the actuarial literature a very efficient and accurate analytical approach to determine risk capitals as an alternative to the current market practice of Monte Carlo simulations. The talk will provide an introduction to Asian option, variable annuity guaranteed benefits as well as basics of risk measures. It should be easily accessible to students who have taken MATH 476 or MATH 567.

2:00 pm   in 241 Altgeld Hall,  Thursday, January 19, 2012
 Del Edit Copy
Submitted by lukyane2.
 Organizational MeetingAbstract: Organizational meeting for the seminar.

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Thursday, January 19, 2012
 Del Edit Copy
Submitted by kapovich.
 John Francis (Northwestern University)Factorization homology of topological manifoldsAbstract: Factorization homology, or the topological chiral homology of Lurie, is a homology theory for manifolds conceived as a topological analogue of Beilinson & Drinfeld's algebraic theory of factorization algebras. I'll describe an axiomatic characterization of factorization homology, à la Eilenberg-Steenrod. The excision property of factorization homology allows one to see factorization homology as a simultaneous generalization of singular homology, the cohomology of mapping spaces, and Hochschild homology. Excision for factorization homology also facilitates a short proof of the nonabelian Poincaré duality of Salvatore and Lurie; this proof generalizes to give a nonabelian Poincaré duality for stratified manifolds, joint work with David Ayala & Hiro Tanaka. Finally, I'll outline work in progress with Kevin Costello, expressing quantum invariants of knots and 3-manifolds in terms of factorization homology.

Friday, January 20, 2012

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Friday, January 20, 2012
 Del Edit Copy
Submitted by kapovich.
 Anthony Várilly-Alvarado (Rice University)Explicit Arithmetic on Algebraic SurfacesAbstract: The geometric complexity of a variety is a good proxy for its arithmetic complexity. Using the classification of algebraic surfaces as a guide for geometric complexity, we will discuss explicit techniques for computing cohomological obstructions to the existence and distribution of rational points on algebraic surfaces, with a view toward identifying a boundary between arithmetically “well-behaved” varieties, like rational surfaces, and arithmetically “wild” varieties, like surfaces of general type.

Monday, January 23, 2012

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Monday, January 23, 2012
 Del Edit Copy
Submitted by kapovich.
 Natalia Saulina (Perimeter Institute for Theoretical Physics, Ontario, Canada)Topological Boundary Conditions and Domain Walls in Abelian Chern-Simons TheoryAbstract: I will classify topological boundary conditions in abelian Chern-Simons theory. The relation between bulk and boundary line operators will be discussed. Further, I will show that domain walls in Chern-Simons theory give consistent gluings of chiral and anti-chiral sectors to form a modular-invariant 2d Rational Conformal Field Theory.

Tuesday, January 24, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, January 24, 2012
 Del Edit Copy
Submitted by franklan.
 Michael Mandell (Indiana University)Localization sequences in THHAbstract: (Joint work with Andrew Blumberg, preprint arXiv:1111.4003.) For a discrete valuation ring R with quotient field F and residue field k, you have a cofibration sequence of K-theory spectra K(k) → K(R) → K(F). The corresponding sequence in THH is not a cofibration sequence, but both the cofiber of the map THH(k)→ THH(R) and the fiber of the map THH(R) → THH(F) have an interpretation in terms of the THH of Waldhausen categories. Thinking in terms of Waldhausen categories, we therefore get two cofibration sequences for THH, THH(k) → THH(R) → THH(F|R) (first constructed by Hesselholt and Madsen) and THH( Spec(R) on Spec(k) ) → THH(R) → THH(F) (generalizing to THH a well-known exact sequence in Hochschild homology). The first arises by looking at enrichments by connective spectra and the second by looking at enrichments in non-connective spectra.

Algebra, Geometry and Combinatoric
2:00 pm   in 345 Altgeld Hall,  Tuesday, January 24, 2012
 Del Edit Copy
Submitted by darayon2.
 Dave Anderson (University of Washington)Arc spaces and equivariant cohomologyAbstract: When an algebraic group acts on a smooth complex variety X, it also acts on the arc space of X, an infinite-dimensional space parametrizing germs of curves in X. In joint work with Alan Stapledon, we develop a new perspective on the equivariant cohomology of X, by replacing X with its arc space. Under certain hypotheses, these infinite-dimensional varieties allow us to obtain a geometric basis (over the integers!) for equivariant cohomology, as well as geometric representatives for cup products as intersections. I'll explain how this leads to a new invariant of singularities, and illustrate our approach with examples from toric varieties and flag varieties.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, January 24, 2012
 Del Edit Copy
Submitted by west.
 Ping Hu (UIUC Math)Upper bounds on the size of $4$- and $6$-cycle-free subgraphs of the hypercubeAbstract: Erdős proposed the problem of determining ex$_Q(n;C_{2t})$, i.e. determining the maximum number of edges that a subgraph of the $n$-dimensional hypercube containing no $2t$-cycle can have. We modify slightly Razborov's flag algebra machinery to be suitable for the hypercube. We use this modified method to show that the maximum number of edges in a subgraph of the $n$-dimensional hypercube containing no $4$-cycle is at most $0.6068$ times the number of edges in the hypercube. For subgraphs containing no $6$-cycle, we improve the upper bound on the proportion of edges from $\sqrt{2}-1$ to $0.3755$. (Joint work with Jozsef Balogh, Bernard Lidicky, and Hong Liu.)

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Tuesday, January 24, 2012
 Del Edit Copy
Submitted by kapovich.
 Jonathan Chaika (University of Chicago)Interval exchange transformationsAbstract: Interval exchange transformations are invertible, piecewise order preserving isometries of the unit interval with finitely many discontinuities. Starting from rotations of the circle, which they generalize, this talk will present their connections to flows on flat surfaces, rational billiards and symbolic coding. Recent results on diophantine approximation for interval exchange transformations will be presented.

Wednesday, January 25, 2012

GEAR Brown Bag
12:00 pm   in 331 Altgeld Hall,  Wednesday, January 25, 2012
 Del Edit Copy
 Abstract: Bring your lunch and join us for informal discussion of all matters relating to GEometric structures And Representation varieties. This week will be introductory and organizational, i.e. even less formal than usual. The GEAR Network will provide cookies.

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Wednesday, January 25, 2012
 Del Edit Copy
Submitted by kapovich.
 Philipp Hieronymi (Department of Mathematics, University of Illinois)Tame geometryAbstract: This talk is an introduction into the study of well-behaved expansions of semialgebraic geometry. I will focus on the classification of such geometries and my contribution to it. In particular, I will discuss new tameness phenomena outside the setting of local finiteness and I will described how a new result that certain classical structures are not tame at all, sheds new light on the question what tameness actually means.

Thursday, January 26, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, January 26, 2012
 Del Edit Copy
Submitted by ford.
 Scott Ahlgren (UIUC Math)Mock modular gridsAbstract: We study infinite grids of mock modular forms which are "dual'' in the sense that while reading across the grid gives the coefficients of the first family, reading down the grid gives the coefficients of the second. Each of these grids contains a generating function of number-theoretic or combinatorial interest as its first entry (for example, the smallest parts" function of Andrews, or a mock theta function of Ramanujan) and we deduce many corollaries for these functions.

Lunch Seminar on NetMath
12:05 pm   in 102 Altgeld Hall,  Thursday, January 26, 2012
 Del Edit Copy
Submitted by gfrancis.
 Debra Woods   [email] (Mathematics/Urbana)History and Vision of NetMathAbstract: NetMath is the distance education program of the Mathematics Department of the University of Illinois (Urbana). Its mission is to extend the high quality curriculum of the Mathematics Department at the University of Illinois to students worldwide. Combining innovative pedagogy with tools tailored to our course offerings, NetMath delivers flexible courses that engage students to learn according to their own schedule and learning style. Conceived by Jerry Uhl, Bill Davis and Horatio Porta, the founders of the Calculus and Mathematica Program, NetMath has grown from a few dozen students to over a thousand annually in the two decades of its existence. NetMath‚Äôs vision is to become the premier university program for all students seeking online math instruction worldwide, continuing to set a high standard for online education, and serving as a center for knowledge exchange and springboard for developing and testing innovative learning technology.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, January 26, 2012
 Del Edit Copy
Submitted by kapovich.
 Robert Craggs (UIUC Math)On doubled 3-manifolds and minimal handle presentations for 4--manifoldsAbstract: We study turning algebraic handle cancellation of certain 2-handle presentations for 4-manifolds of the form $M_* \times [-1,1]$ into geometric handle cancellations. Algebraic here refers to extended Nielsen invariants on group presentations, We show how the cancellation problems leads to obstruction problems involving framed surgery on 3-manifolds. We will report on efforts to calculate some surgery obstructions

2:00 pm   in 241 Altgeld Hall,  Thursday, January 26, 2012
 Del Edit Copy
Submitted by lukyane2.
 Mee Seong Im (UIUC Math)The Hamiltonian reduction of a certain affine variety Abstract: I will discuss certain theories in symplectic geometry and in algebraic geometry which give us various ways to view the same complex manifold. More specifically, the Hamiltonian reduction of the cotangent bundle of a certain variety can be thought of as the symmetric product of the complex plane while the GIT quotient of the same cotangent bundle but which is twisted by a character of the general linear group can be thought of as a certain Hilbert scheme. These varieties are related by the Hilbert-Chow morphism in the sense that one is a desingularization of the other. I will end with an analogous construction in which a notion of noncommutativity appears in the algebro-geometric quotient. Lots of examples will be provided throughout my talk.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, January 26, 2012
 Del Edit Copy
Submitted by beder.
 Organizational Meeting

5:00 pm   in 241 Altgeld Hall,  Thursday, January 26, 2012
 Del Edit Copy
Submitted by funk3.
 Austin Rochford (UIUC Math)Amenability Across AnalysisAbstract: Part one of a two part talk. We will define amenable groups and explore generalizations of amenability to various areas of analysis. This week we will consider harmonic analysis and ergodic theory.

Friday, January 27, 2012

Women's Seminar
11:00 pm   in Altgeld Hall,  Friday, January 27, 2012
 Del Edit Copy
Submitted by funk3.
 Beginning of Semester LunchAbstract: We will have our traditional beginning of the semester lunch on Friday. We will meet in the mailroom at 11:00 am. We will walk over to the Illini Union Ballroom and be prepared to be seated as soon as they open at 11:30. In the meantime, we will have time to chat about the upcoming semester. Jane and Kelly have some ideas floating around and we'd like to get your feedback. We'll be in the Ballroom until 12:30. So, if you have class at 12:00, you can duck out early from lunch, or if you get out of class at 11:50, you can join us after your class.

Tuesday, January 31, 2012

Number Theory
11:00 am   in 241 Altgeld Hall,  Tuesday, January 31, 2012
 Del Edit Copy
Submitted by berndt.
 James Sellers (Pennsylvania State University)On m–ary Partitions and Non-Squashing Stacks of BoxesAbstract: The focus of this talk will be on congruences (divisibility properties) satisfied by various integer partition functions. I will share some history, starting with Ramanujan's groundbreaking work in the 1910's on the unrestricted partition function p(n) and moving rapidly to work by Robert Churchhouse in the late 1960's on the binary partition function. I will also discuss work of Oystein Rodseth, George Andrews, and Hansraj Gupta in the 1970's on results for m-ary partitions which are natural generalizations of binary partitions. (An m-ary partition of a positive integer n is a nonincreasing sequence of powers of m which sum to n.) I will then discuss recent work I completed with Rodseth which generalizes the results of Andrews and Gupta from the 1970's. I will close with a set of "applications" of m-ary partitions to Neil Sloane's questions on non-squashing stacks of boxes.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, January 31, 2012
 Del Edit Copy
Submitted by franklan.
 Claire Tomesch (University of Chicago)Categories of cohesion and ‘discretized’ model categoriesAbstract: The purpose of this talk is to describe a notion of category of cohesion -- a concept of Lawvere introduced to describe 'relative discreteness' -- and its role in defining and understanding a model structure on Simpson-Tamsamani style versions of weak n-categories. The main payoff of this approach is an iterable construction of a model structure which takes into account the special role of 'discrete' objects.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, January 31, 2012
 Del Edit Copy
Submitted by tzirakis.
 Aynur Bulut (Institute for Advanced Study)The defocusing energy-supercritical cubic nonlinear wave equationAbstract: In this talk , we will discuss some recent results on global well-posedness and scattering for the defocusing cubic nonlinear wave equation (NLW) treating the energy-supercritical regime, that is dimensions five and higher. More precisely in a series of works (first in dimensions six and higher for general data, in dimension five with radial data and, very recently, in dimension five for general data) we prove global well-posedness under an a priori uniform in time control of the critical Sobolev norm by establishing strong integrability and regularity properties for a particular class of solutions to NLW. In particular, we will focus on our recent work in dimension five in the case of the general data.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, January 31, 2012
 Del Edit Copy
Submitted by ssolecki.
 Dan Grayson (UIUC)Voevodsky's new foundations for mathematicsAbstract: Voevodsky's "Homotopy Type Theory" uses topology to provide new models for checking the consistency of a "type theory" close to what is currently implemented in the mathematical proof-checking computer program "coq". The new models allow the introduction of new axioms into the theory. These ideas promise to dramatically simplify the computerized checking of the proofs of modern mathematics, perhaps inaugurating the era where mathematicians commonly check their work as they proceed. In this talk a relative newcomer to the field will give an elementary account of the new theory and explain what it has to do with topology.

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, January 31, 2012
 Del Edit Copy
Submitted by kkirkpat.
 Joseph Conlon   [email] (U Michigan Math)Strong Central Limit Theorems in Elliptic and Parabolic PDE with random coefficientsAbstract: In this talk I will discuss some recent work of myself in collaboration with Tom Spencer and Arash Fahim. The basic object of study is uniformly elliptic and parabolic PDE in divergence form with random coefficients. It has been known since the 1980's that under suitable scaling the solutions of these equations converge in distribution to the solution of a constant coefficient PDE, the so called homogenized equation. In the talk I shall describe our results on the rate of convergence in homogenization when the random environment is a uniformly elliptic Euclidean Field Theory. The main tools needed to prove these theorems are the Poincare inequality and the Calderon-Zygmund theorem on boundedness in L^p of Fourier multipliers.

Algebra, Geometry and Combinatoric
2:00 pm   in 345 Altgeld Hall,  Tuesday, January 31, 2012
 Del Edit Copy
Submitted by darayon2.
 Jenna Rajchgot (Cornell)Compatibly split subvarieties of the Hilbert scheme of points in the planeAbstract: Consider the Hilbert scheme of n points in the affine plane and the divisor "at least one point is on a coordinate axis". One can intersect the components of this divisor, decompose the intersection, intersect the new components, and so on to stratify the Hilbert scheme by a collection of reduced (indeed, "compatibly Frobenius split") subvarieties. This may prompt one to ask, "What are these subvarieties?" or, better, "What are all of the compatibly split subvarieties?" I'll begin by providing the answer for some small values of n. Following this, I'll restrict to a specific affine patch (now for arbitrary n) and describe a degeneration of the compatibly split subvarieties to Stanley-Reisner schemes.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, January 31, 2012
 Del Edit Copy
Submitted by west.
 Jozsef Balogh (UIUC Math)The biggest loserAbstract: An important trend in Combinatorics in recent years has been the formulation and proof of various sparse analogues' of classical extremal results in Graph Theory and Additive Combinatorics. Due to the recent breakthroughs of Conlon and Gowers, and Schacht, many such theorems, e.g., the theorems of Turán and Erdős and Stone in extremal graph theory, and the theorem of Szemerédi on arithmetic progressions, are now known to extend to sparse random sets. I give a survey on the recent developments. (Joint work with Robert Morris and Wojtek Samotij.)

Wednesday, February 1, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, February 1, 2012
 Del Edit Copy
Submitted by seminar.
 Joseph Rosenblatt (Department of Mathematics, University of Illinois)Averaging over Rectangles in Euclidean Spaces

Thursday, February 2, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by ford.
 Daniel Fiorilli (IAS Princeton)On how the first term of an arithmetic progression can influence the distribution of an arithmetic sequenceAbstract: We will show that many arithmetic sequences have asymmetries in their distribution amongst the progressions mod q. The general phenomenon is that if we fix an integer a having some arithmetic properties (these properties depend on the sequence), then the progressions a mod q will tend to contain fewer elements of the arithmetic sequence than other progressions a mod q, on average over q. The observed phenomenon is for quite small arithmetic progressions, and the maximal size of the progressions is fixed by the nature of the sequence. Examples of sequences falling in our range of application are the sequence of primes, the sequence of integers which can be represented as the sum of two squares (or more generally by a fixed positive definite binary quadratic form) (with or without multiplicity), the sequence of twin primes (under Hardy-Littlewood) and the sequence of integers free of small prime factors. We will focus on these examples as they are quite fun and enlightening.

Lunch Seminar on NetMath
12:05 pm   in 102 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by gfrancis.
 Bruce Carpenter   [email] (Mathematics/Urbana)The Pedagogy of NetMathAbstract: The NetMath online instructional model attempts to integrate three things: courseware designed to help students learn mathematics by dynamic exploration and visualization, the incorporation of a computer algebra system for students to perform calculations and write full explanations of their solution process, and a learning management system to streamline administration of the course and promote communication between students, instructors, and mentors. We will discuss each of these in detail by presenting the current system and its challenges as well as surveying possible innovations to improve instruction.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by kapovich.
 Albert Fisher (University of Sao Paulo)A flow crossection for Moeckel's theorem on continued fractionsAbstract: We construct a cross-section to the principal congruence modular flow which is represented as a skew product transformation over the natural extension of the Gauss map. This leads to a new proof of Moeckel's theorem on rational approximants. For an irrational number $x$ in the unit interval with continued fraction expansion $[n_0 n_1...]$, let $p_k/q_k=$[n_0 n_1..n_k] be the rational approximants for $x$. Writing these in lowest terms, they can be of three types: $\frac{O}{E}$, $\frac{E}{O}$, or $\frac{O}{O}$ where $O$ stands for odd and $E$ for even. Moeckel's theorem states that the frequency of each of these exists almost surely. What is unusual in the proof is that this does not follow directly from the ergodic theorem applied to an observable on the Gauss map (the shift on continued fractions): one must first enlarge the space. Moeckel's approach makes use of the geodesic flow on a three-fold cover of the modular surface, together with a geometric argument for counting the time that geodesics spend in cusps. Ergodicity of the flow is automatic (via the Hopf argument) but the counting is somewhat involved. Later Jager and Liardet found a second purely ergodic theoretic proof, constructing a skew product over the Gauss map. There the counting is direct, but the proof of ergodicity is more difficult. Our proof unifies the two earlier arguments, inheriting these strong points of each.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by aimo.
 Robert Kaufman (UIUC Math)Renorming of Banach spaces - a metrical propertyAbstract: A bounded set S in a metric space has a radius, defined by closed disks containing S. When the infimum of radii is realized by a closed disk, S is "centered". Theorem: A nonreflexive Banach space X can be renormed so that some set {a,b,c} in X is not centered. This provides a second (or third) proof of the renorming theorem of W. Davis and W. Johnson (1973).

2:00 pm   in 241 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by lukyane2.
 Ser-Wei Fu (UIUC Math)Length Spectra and Deformation FamiliesAbstract: This is a practice talk for the preliminary exam. I will define and describe the spectral rigidity problem and talk about known results. The talk will be focused on clearly defining every object and giving examples to illustrate a new approach to the problem. To be specific, two main topics that will be discussed are flat metrics and train tracks on surfaces.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by beder.
 Howard Osborn (UIUC Math)New Facets of Kaehler DerivativesAbstract: If a commutative algebra over a field of characteristic zero is isomorphic to a function algebra with values in the field, and if the unit element is the only nonzero idempotent, then the universal Kaehler derivative annihilates only the elements that correspond to constant functions. This result is used to show that the cotangent spaces of the algebra are mutually isomorphic, and that such an algebra has the analog of a smooth atlas, hence a smooth structure, if and only if the Kaehler module is reflexive.

5:00 pm   in 241 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by funk3.
 Austin Rochford (UIUC Math)Amenability Across Analysis: Part IIAbstract: Part two of a two part talk. We will explore generalizations of amenability to various areas of analysis. This week we will consider harmonic analysis and banach algebras.

Friday, February 3, 2012

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, February 3, 2012
 Del Edit Copy
Submitted by phierony.
 Ward Henson (UIUC)Continuous model theory and Gurarij's universal homogeneous separable Banach spaceAbstract: Gurarij’s Banach space was constructed in the 1960s using a metric version of a Fraïssé construction; it is universal isometrically (for separable Banach spaces) and homogeneous in an almost-isometric sense relative to its finite dimensional subspaces. It is the analogue (for Banach spaces) of such structures as the random graph and Urysohn’s metric space. General results in Banach space theory from the 1960s show that its dual space is of the form $L^1(\mu)$ for some measure $\mu$, so it falls into the important class of classical Banach spaces,’’ a fact that is far from obvious based on the original construction. Wolfgang Lusky showed in the 1970s that the Gurarij space is isometrically unique, a surprising result. He also indicated that the set of smooth points of norm 1 is an orbit of its automorphism group. In this talk it will be shown how these results can be seen and improved using continuous model theory. In particular, the class of separable Gurarij spaces can be realized as the class of separable models of a certain continuous theory $T$ (of unit balls of Banach spaces); this theory has quantifier elimination and is the model completion of the theory of all Banach spaces. An optimal amalgamation result due to the speaker yields a simple formula for the induced metric on the type spaces of $T$ over sets of parameters, which is the key to the applications that will be discussed in this talk. A highlight of recent research, proved in joint work with Itaï Ben Yaacov, is the following: let $X$ be Gurarij's space and let $E$ be a finite dimensional space whose unit ball is polyhedral (i.e., the convex hull of a finite set). There is an isometric linear embedding $S$ of $E$ into $X$ such that $S(E)$ has the unique Hahn-Banach extension property in $X$; moreover, the set of all such embeddings forms a full orbit under the action of the automorphism group of $X$. Model-theoretically this situation is equivalent to saying that $(X,a)_{a \in S(E)}$ is an atomic model of its theory.

Tuesday, February 7, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, February 7, 2012
 Del Edit Copy
Submitted by franklan.
 Nathaniel Stapleton (MIT)Transchromatic twisted character mapsAbstract: The ring of coefficients of the codomain of the transchromatic generalized character maps is constructed to be the universal extension of the K(t)-localization of Morava En over which the p-divisible group associated to En splits as a sum of a height t connected p-divisible group and a height n-t constant p-divisible group. We will describe a refinement of this story to the universal extension of En over which the p-divisible group is a non-trivial extension of a height t connected p-divisible group by a height t constant p-divisible group. This refinement is able to recover the transchromatic generalized character maps and also recovers the classical generalized character theory of Hopkins, Kuhn, and Ravenel when t=0.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 7, 2012
 Del Edit Copy
Submitted by ssolecki.
 Robert Kaufman (UIUC)Hurewicz's Theorem on Uncountable Close Sets--A DetourAbstract: When M is an uncountable, compact metric space the uncountable, closed subsets of M form an analytic, non-Borel set. We present a variant of this, relying on the notion of ultrametric space. Time permitting, we review the original proof, and suggest an alternative based on earlier work of Mazurkiewicz and Sierpin'ski.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, February 7, 2012
 Del Edit Copy
Submitted by kkirkpat.
 Jonathan Weare   [email] (U Chicago Math)A modified diffusion Monte Carlo and other ensemble sampling methodsAbstract: This talk will survey my efforts with coworkers to develop and analyze Monte Carlo sampling algorithms for complex (usually high dimensional) probability distributions. These sampling problems are typically difficult because they have multiple high probability regions separated by low probability regions and/or they are badly scaled in the sense that there are strong unknown relationships between variables. I'll begin the talk by discussing a simple modification of the standard diffusion Monte Carlo algorithm that results in a more efficient and much more flexible tool for use, for example, in rare event simulation. If time permits I'll discuss a few other ensemble based sampling tools designed to directly address energy barriers and scaling issues.

Geometry Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, February 7, 2012
 Del Edit Copy
Submitted by sba.
 Dick Bishop (UIUC)Comparison geometry, total curvature, pursuit-evasionAbstract: (Joint work with S. Alexander and R. Ghrist.) After a review of comparison geometry, total curvature, and pursuit-evasion in CAT(0) spaces, the properties of pursuit flow, particularly its invariant conics (see Figure), for an evader tracking a line in the plane will be examined. A comparison for a pursuer of an evader tracking a geodesic in a CAT(0) space is given. More generally, any evader curve of finite total curvature in a CAT(0) can be developed to a curve in the plane with the same total curvature on all corresponding segments and there is a comparable pursuit flow in the plane.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 7, 2012
 Del Edit Copy
Submitted by west.
 Robert Jamison (UIUC Math and Clemson University)Sum-Tolerance Graphs with Eutactic RankAbstract: This talk will focus on certain classes of rank-tolerance graphs that generalize the co-threshold-tolerance (co-TT) graphs introduced by Monma, Reed, and Trotter. In a rank-tolerance representation of a graph, each vertex is assigned two parameters: a rank, which represents the size of that vertex, and a tolerance, which represents an allowed extent of conflict with other vertices. Two vertices are adjacent if and only if their joint rank exceeds (or equals) their joint tolerance. This study is motivated by the class SP of sum-product graphs, introduced by Golumbic and RJ, where the tolerance coupling function is the sum of the two tolerances and and the rank coupling function is the product of the two ranks. Many properties of sum-product graphs remain valid when product is replaced by a general eutactic function --- one that satisfies a certain convexity condition. The class of eutactic functions is quite broad. For example, it includes all symmetric polynomials (in two variables) with positive coefficients. We show that SP strictly contains co-TT as well as all complete bipartite graphs $K_{2,n}$, and we survey a number of other results. My advisor Victor Klee vowed as graduate student that he would avoid formulae involving binomial coefficients. I vowed that I would never get involved with multidimensional calculus. In the talk I will explain (briefly) why we were both wrong.

Women's Seminar
4:00 pm   in 241 Altgeld Hall,  Tuesday, February 7, 2012
 Del Edit Copy
Submitted by funk3.
 Sogol Jahanbekam (UIUC Math)Application of Combinatorial Nullstellensatz to graph factor and the 1,2-Conjecutre; Dynamic coloring of grids; Antiramsey TheoryAbstract: I will first talk about applications of Combinatorial Nullstellensatz to graph factors, the 1,2-Conjecture, and the 1,2,3-Conjecture. I'll give some sufficient conditions for a graph to have a specified factor and sufficient conditions with respect to minimum degree and chromatic number such that the 1,2-Conjecture or the 1,2,3-conjecture hold for the graph. Next subject will be about r-dynamic coloring of grids, and finally I will introduce a future aim in Antiramsey Theory.

Wednesday, February 8, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, February 8, 2012
 Del Edit Copy
Submitted by seminar.
 William Haboush (Department of Mathematics, University of Illinois)What is a root system?

Thursday, February 9, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 9, 2012
 Del Edit Copy
Submitted by ford.
 Jimmy Tseng (UIUC Math)Bounded Luroth expansionsAbstract: Luroth series expansions are in a family of various expansions of the real numbers, a family which includes continued fractions. Like for continued fractions, every real number can be expressed as a Luroth expansion. Also like for continued fractions, the digits of a Luroth expansion are generated by a self-map, the Luroth map. The digits are, of course, an encoding of the map and give us a geometric way of looking at the expansion. I will give a sketch of the proof of the following result (joint with B. Mance): the set B of numbers with bounded Luroth expansion, bounded continued fraction expansion, and bounded n-ary expansion for every integer n > 1 is a dense set of full Hausdorff dimension. (Each of these conditions on B would form a superset of zero Lebesgue measure.) The proof is based on applying a technique developed by W. Schmidt (or a later variant made by C. McMullen) to the Luroth map,which has infinite distortion, and is adapted from techniques that I developed in 2009 for cases of bounded distortion.

Lunch Seminar on NetMath
12:05 pm   in 102 Altgeld Hall,  Thursday, February 9, 2012
 Del Edit Copy
Submitted by gfrancis.
 Pat Szuta   [email] (Mathematics/Urbana)IT Innovations in Online Math Development and InstructionAbstract: The University of Illinois has a long history of creating tools for effectively instructing mathematics online. These home-grown systems are often necessary because mathematics rarely fits into industry standards of online instruction. We will discuss how many of the challenges of teaching math online are rooted in technology, and what is currently being done to solve them.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 9, 2012
 Del Edit Copy
Submitted by kapovich.
 Catherine Pfaff (Rutgers - Newark)Constructing and Classifying Fully Irreducible Outer Automorphisms of Free GroupsAbstract: The main theorem of my thesis emulates, in the context of $Out(F_r)$ theory, a mapping class group theorem (by H. Masur and J. Smillie) that determines precisely which index lists arise from pseudo-Anosov mapping classes. Since the ideal Whitehead graph gives a finer invariant in the analogous setting of a fully irreducible $\phi \in Out(F_r)$, we instead focus on determining which of the 21 connected 5-vertex graphs are ideal Whitehead graphs of ageometric, fully irreducible $\phi \in Out(F_3)$. Our main theorem accomplishes this. The methods we use for constructing fully irreducible $\phi\in Out(F_r)$, as well as our identification and decomposition techniques, can be used to extend our main theorem, as they are valid in any rank. Our methods of proof rely primarily on Bestvina-Feighn-Handel train track theory and the theory of attracting laminations.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, February 9, 2012
 Del Edit Copy
Submitted by aimo.
 Kevin Wildrick (University of Bern)Lipschitz constants and differentiability almost everywhereAbstract: Rademacher's theorem that Lipschitz functions are differentiable almost everywhere forms the backbone of results in function theory, geometric measure theory, and geometric topology. A prime example is Cheeger's theorem regarding the existence of differentiable structures on metric spaces supporting a Poincaré inequality. We will review some classical results and then discuss a version of Rademacher's theorem for the "lower" Lipschitz constant, which detects oscillation only on some sequence of scales tending to zero, rather than on all sequences of scales tending to zero. We also provide an example showing the sharpness of the results and the relationship of differentiability to the capacity of points.

2:00 pm   in 241 Altgeld Hall,  Thursday, February 9, 2012
 Del Edit Copy
Submitted by lukyane2.
 Michael DiPasquale (UIUC Math)Resolutions and GeometryAbstract: Given a variety X inside of some projective space, one of the primary ways in which algebraic geometers study X is through its homogeneous coordinate ring S_X. One way to unpack the information hiding mysteriously inside of S_X is to study the free resolution of S_X. From this resolution come many fantastic invariants of X, primarily the betti diagram of X from which one can compute the Hilbert function of X and the regularity of X. Many difficult open conjectures for curves relate to the configuration of the betti diagram of the curve. Our modest goal is to see how such a seemingly arcane algebraic object as a resolution can actually reflect the geometry of a variety, primarily by looking at the case where X is a bunch of points in projective space. Interested folks may find David Eisenbud's book Geometry of Syzygies a good read; that is where much of my material will come from.

Tuesday, February 14, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, February 14, 2012
 Del Edit Copy
Submitted by jathreya.
 Albert Fisher (University of Sao Paolo)Invariant measures for adic transformations on Bratteli diagrams Abstract: Vershik's adic transformations are a class of combinatorially defined maps that can be used to topologically and measure-theoretically model a wide variety of dynamical systems, including substitution dynamical systems, cutting-and-stacking constructions and interval exchange transformations. They act on the path space of a Bratteli diagram, defined by a sequence of nonnegative integer matrices and so generalizing subshifts of finite type to nonstationary combinatorics. Let us say a matrix sequence is primitive if for all $k$ there exists $n>k$ such that $M_k... M_n> 0$. Primitivity implies minimality (that every orbit is dense) for adic transformations, but in the nonstationary case, unique ergodicity (that there is a unique unvariant probability measure) does not always follow. In recent work we classify the invariant Borel measures which are finite positive on the path space of some sub-Bratteli diagram, for the bounded alphabet but not necessarily primitive case. This includes some interesting (and naturally occuring) measures which are infinite on every open subset. Our results extend theorems of Bezuglyi, Kwiatkowski, Medynets and Solomyak. This is joint work with Marina Talet, Universite de Provence.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, February 14, 2012
 Del Edit Copy
Submitted by franklan.
 Thomas Kragh (MIT)Stable homotopy types and orientations in Hamiltonian Floer theoryAbstract: I will start by outlining the basic ideas in Morse theory and Conley index theory. Then I will describe Hamiltonian Floer homology using infinite dimensional Morse homology. I will then describe the ideas of finite dimensional approximations, and discuss existence and uniqueness. For cotangent bundles these finite dimensional approximations exists canonically - but are not natural. I will explain this in more detail for a nearby Lagrangian, and describe how this lead to new insights into the coherent orientations in Floer homology. If time permits I will talk about some generalizations of the finite dimensional approximations and relations to complex periodic cobordism.

Geometry Seminr
2:00 pm   in 243 Altgeld Hall,  Tuesday, February 14, 2012
 Del Edit Copy
Submitted by sba.
 Joseph Rosenblatt (UIUC )Distribution of parameters in optimal approximationsAbstract: Given a compact $d$-dimensional manifold with boundary, the computation of its $d$-dimensional volume can be carried out by approximating it by simpler manifolds for which the volume calculation is easy. This is the classical approach that is often used to define the volume of the manifold. The choice of optimal approximations for this purpose raises some interesting geometrical issues. Here is a very simple case. Take an increasing smooth function $f$ on $[0,1]$ and choose a partition $P_n$ of $[0,1]$ containing $n$ points for which the lower Riemann sum gives the best approximation of $\int_0^1 f(s)\, ds$ among all possible partitions containing just $n$ points. How are the points of $P_n$ distributed? For example, if $P_n =(x_k:k=1,\dots,n)$, and we take the discrete measure $\mu_n = \frac 1n\sum_{k=1}^n \delta_{x_k}$, does the sequence $(\mu_n)$ converge weakly as $n\to \infty$? If so, what is its limit?

Algebraic Geometry
3:00 pm   in 243 Altgeld Hall,  Tuesday, February 14, 2012
 Del Edit Copy
Submitted by schenck.
 Wenbo Niu   [email] (Purdue)Asymptotic Regularity of Ideal SheavesAbstract: Let $I$ be an ideal sheaf on $\mathbb{P}^n$ . Associated to $I$ there are three elementary invariants: the invariant $s$ which measures the positivity of $I$, the minimal number $d$ such that $I(d)$ is generated by its global sections, and the Castelnuovo-Mumford regularity reg $I$. In general one has $s \leq d\leq \mbox{reg }I$. If we consider the asymptotic behavior of the regularity of $I$, that is the regularity of $I^p$ when $p$ is sufficiently large, then we could have a clear picture involving these invariants. We will talk about two main theorems in this direction. The first one is the asymptotic regularity of $I$ is bounded by linear functions as $sp\leq \mbox{reg }I^p\leq sp+e$, where $e$ is a constant. The second one is that if $s=d$, i.e., $s$ reaches its maximal value, then for $p$ large enough reg $I^p=dp+e$ for some positive constant $e$.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 14, 2012
 Del Edit Copy
Submitted by west.
 Gexin Yu (College of William and Mary)Degree bounds on coloring graphs equitably and defectivelyAbstract: A graph has an equitable, defective $k$-coloring (an ED-$k$-coloring) if there is a $k$-coloring of $V(G)$ that is 1-defective (every vertex shares its color with at most one neighbor) and equitable (the sizes of color classes differ by at most one). We prove an analogue of the Hajnal-Szemerédi Theorem: Every graph with maximum degree $D$ can be ED-$k$-colored for $k\ge D$. When the maximum degree is large, we prove that far fewer colors suffice.

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Tuesday, February 14, 2012
 Del Edit Copy
Submitted by kapovich.
 P. Di Francesco (Institut de Physique Theorique, CEA Saclay and Mathematical Sciences Research Institute, Berkeley, CA)Discrete Integrable Systems and Cluster AlgebrasAbstract: Recursive systems arising from integrable quantum spin chains, such as Q,T and Y-systems display remarkable combinatorial properties. These are actually part of a more general mathematical structure called Cluster Algebras, introduced by Fomin and Zelevinsky around 2000, and which has found a host of mathematical applications so far, ranging from the theory of total positivity, Teichmüller space geometry, to the representation theory of quantum groups. A cluster algebra is a sort of dynamical system describing the mutation of a vector of data along the edges of an infinite tree, with rules guaranteeing that only Laurent polynomials of the initial data are generated. A longstanding conjecture of Fomin and Zelevinsky states that these have non-negative integer coefficients. In this talk, we will describe the very simple example of discrete integrable systems, and use their exact solutions in terms of paths on graphs or networks to explain this positive Laurent phenomenon. Non-commutative extensions will also be discussed.

Wednesday, February 15, 2012

Study Seminar in Geometry and Analysis
3:00 pm   in 347 Altgeld Hall,  Wednesday, February 15, 2012
 Del Edit Copy
Submitted by jathreya.
 Organizational MeetingAbstract: We'll be chatting about the papers we're going to discuss this semester. Possibilities include: 1) Witten's Gauge theoretic interpretation of Kovanov homology of knots (these are they same equations he proposed for Geometric Langlands) 2) Extremals of the determinant of the Laplacian and uniformization. In dimension 2 the fundamental paper would be the one by Osgood, Phillips and Sarnak: http://www-ee.stanford.edu/~osgood/papers/extremals1988.pdf 3)Manning's work on the behavior of volume growth entropy along Ricci Flow in the setting of surfaces.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, February 15, 2012
 Del Edit Copy
Submitted by seminar.
 Peter Loeb (Department of Mathematics, University of Illinois)Infinitesimals in Analysis and Probability TheoryAbstract: The notion of an infinitesimal quantity has been used in mathematics for over 2200 years. It eluded rigorous treatment until the work using model theory of Abraham Robinson in 1960 established a rigorous foundation for the use of infinitesimals in mathematics. Recent extensions and applications of his theory, now called nonstandard analysis, have produced new results in many areas including operator theory, stochastic processes, mathematical economics and mathematical physics. In all of these areas, infinitely small and infinitely large quantities can play an essential role in the creative process. At the level of calculus, the integral can now be correctly defined as the nearest ordinary number to an infinitely large sum of infinitesimal quantities. In Probability theory, Brownian motion can now be rigorously parameterized by a random walk with infinitesimal increments. In economics, an ideal economy can be formed from an infinite number of agents each having an infinitesimal influence on the economy. Spaces formed with nonstandard analysis give the simplest probability spaces for a continuum of independent random variables or traders in an economy. The talk gives an introduction to this fruitful area of mathematics.

Thursday, February 16, 2012

Number Theory Seminar
11:00 am   in 243 Altgeld Hall,  Thursday, February 16, 2012
 Del Edit Copy
Submitted by ford.
 Youness Lamzouri (UIUC Math)Conditional bounds for the least quadratic non-residue and the values of L-functions at 1Abstract: We study explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic non-residue and the least prime in an arithmetic progression. We also refine the classical conditional bounds of Littlewood for $L$-functions at $s=1$. In particular, we derive explicit upper and lower bounds for $L(1,\chi)$ and $\zeta(1+it)$, and deduce explicit bounds for the class number of imaginary quadratic fields. This is a joint work with X. Li and K. Soundararajan.

Lunch Seminar on NetMath
12:05 pm   in 102 Altgeld Hall,  Thursday, February 16, 2012
 Del Edit Copy
Submitted by gfrancis.
 Gloriana Gonzalez   [email] (Curriculum & Instruction, Urbana)Resources for Building a Collective Memory in the Online Geometry CourseAbstract: The talk examines components in the design of the online geometry course that support students' remembering of geometric concepts and procedures. These components include the recording of class discussions of proofs. The talk examines how the use of these novel and interactive resources could enable students to navigate through the online materials differently than when working with a textbook in a traditional face-to-face course. I will argue that these components help to create a collective memory of students' experiences course and of the mathematical knowledge that they are supposed to learn in the online geometry course.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 16, 2012
 Del Edit Copy
Submitted by kapovich.
 Richard Brown (Johns Hopkins University)The dynamics of mapping class actions on the character varieties of surfacesAbstract: We construct an algebraic model of the special linear character variety of a compact surface in a way which facilitates the study of the action of the mapping class group of the surface on the affine set. We then present some early results of this study, and discuss some intended directions of further study.

2:00 pm   in 241 Altgeld Hall,  Thursday, February 16, 2012
 Del Edit Copy
Submitted by lukyane2.
 Jimmy Shan (UIUC Math)Polytopes, zeroes of polynomial equations and mixed volumeAbstract: We will present a bound of number of zeroes of polynomial equations using mixed volumes of polytopes which are constructed from the exponent vectors of the polynomials; Newton polytope associated to one polynomial is a prototype.

5:00 pm   in 147 Altgeld Hall,  Thursday, February 16, 2012
 Del Edit Copy
Submitted by funk3.
 Steve Avsec (UIUC Math)A Characterization of Noncommutative Brownian MotionAbstract: We will discuss what noncommutative brownian motion is and how it resembles classical brownian motion. I will then give the characterization which is based on a generalized Fock space construction given by certain positive definite function on the infinite symmetric group.

Friday, February 17, 2012

Harmonic Analysis and Differential Equations
1:00 pm   in 343 Altgeld Hall,  Friday, February 17, 2012
 Del Edit Copy
Submitted by verahur.
 Mat Johnson (University of Kansas)Stability of Periodic Wave Trains in a Kuramoto-Sivashinsky EquationAbstract: (NOTE UNUSUAL DATE AND TIME) In this talk, we consider the spectral and nonlinear stability of periodic traveling wave solutions of a dispersion modified Kuramoto-Sivashinsky equation modeling viscous thin film flow down an inclined plane. In special cases, it has been known (with varying levels of rigor) since 1976 that, when subject to weak localized perturbations, spectrally stable solutions of this form exist. Although numerical time evolution studies indicate that these waves should also be nonlinearly stable to such perturbations, an analytical verification of this result has only recently been provided. In this talk, I will discuss a nonlinear stability theory for such spectral stability periodic wave trains, as well as the numerical and analytical verification of the required spectral stability and structural hypothesis of this theorem in particular canonical limits of dispersion/dissipation. This is joint work with Blake Barker and Kevin Zumbrun (Indiana University), as well as Pascal Noble and L. Miguel Rodrigues (University of Lyon I).

Logic Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, February 17, 2012
 Del Edit Copy
Submitted by ssolecki.
 Kostya Slutsky (UIUC)Two-sided invariant metrics on HNN extensionsAbstract: We discuss some technical properties of the Graev metrics on the free products of groups with two-sided invariant metrics and will sketch the construction of the the two-sided invariant metrics on HNN extensions of groups of bounded diameter.

Monday, February 20, 2012

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Monday, February 20, 2012
 Del Edit Copy
Submitted by kapovich.
 Benjamin Brubaker (MIT)Whittaker coefficients of Eisenstein seriesAbstract: The (Fourier-)Whittaker coefficients of Eisenstein series for reductive groups were explored by Langlands, whose computation of their constant terms partly inspired his famous functoriality conjectures. Since then, Whittaker coefficients of automorphic forms have played a starring role in the theory of L-functions and we discuss a few highlights. Much of this picture generalizes to certain finite covers of reductive groups, where we find surprising new expressions for the Whittaker coefficients of Eisenstein series involving crystal graphs and statistical mechanics. We'll define all of these terms in the course of the talk and argue by simple examples beginning with the zeta function, and is intended to be accessible to a wide audience. (This is joint work with various combinations of Dan Bump, Sol Friedberg, and Tony Licata)

Tuesday, February 21, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, February 21, 2012
 Del Edit Copy
Submitted by jathreya.
 David Aulicino (Maryland)Teichmueller Disks with Completely Degenerate Kontsevich-Zorich SpectrumAbstract: The moduli space of genus $g$ Riemann surfaces is the space of all complex structures on a closed orientable surface of genus $g$ up to orientation preserving diffeomorphisms. The Teichmueller geodesic flow is the flow on the cotangent bundle of the Teichmueller space of surfaces defined by the direction of minimal dilatation and it descends to the cotangent bundle of the moduli space under the action of the mapping class group. It is well-known that the Lyapunov spectrum of this flow is determined by $g$ numbers $$1 = \lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_g \geq 0.$$ The Kontsevich-Zorich conjecture, proven by Forni and Avila-Viana, showed that generically all the inequalities are strict with respect to the canonical absolutely continuous measures. However, Forni found an example of a measure on the genus three moduli space, and Forni-Matheus found a measure in genus four, with completely degenerate spectrum, i.e. $$1 = \lambda_1 > \lambda_2 = \cdots = \lambda_g = 0.$$ We prove that these are the only such measures in genus three and four. Furthermore, there are no such measures for $g=2$ and $g \geq 13$. Finally, if there are no square-tiled surfaces in genus five that determine a measure with completely degenerate spectrum, then there are no examples for $g \geq 5$.

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, February 21, 2012
 Del Edit Copy
Submitted by ford.
 Benjamin Brubaker (MIT Math)Statistical mechanical models and L-functionsAbstract: Local L-functions arise naturally as matrix coefficients for certain infinite dimensional representations. We'll briefly review some of these constructions, but then discuss how the results are expressible in terms of two-dimensional statistical mechanics. This subject has a easily comprehensible combinatorial structure which we will make use of in order to prove functional equations for the corresponding L-functions.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, February 21, 2012
 Del Edit Copy
Submitted by franklan.
 Nathaniel Rounds (Indiana University)Compactifying string topologyAbstract: String topology studies the algebraic topology of the free loop space of a manifold. In this talk, we describe a compact space of graphs and show how this space gives algebraic operations on the singular chains of the free loop space. In particular, our chain level operations induce Cohen and Godin's "positive boundary TQFT" on the homology the free loop space. This project is joint work with Kate Poirier.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, February 21, 2012
 Del Edit Copy
Submitted by berdogan.
 William Green (Eastern Illinois University)Dispersive estimates for Schrodinger operators in dimension two

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 21, 2012
 Del Edit Copy
Submitted by ssolecki.
 Ward Henson (UIUC)Uncountably categorical Banach space structuresAbstract: Model theory is applied to (unit balls of) Banach spaces (and structures based on them) using the $[0,1]$-valued continuous version of first order logic. A theory $T$ of such structures is said to be $\kappa$-categorical if $T$ has a unique model of density $\kappa$. Work of Ben Yaacov and Shelah-Usvyatsov shows that Morley's Theorem holds in this context: if $T$ has a countable signature and is $\kappa$-categorical for some uncountable $\kappa$, then $T$ is $\kappa$-categorical for all uncountable $\kappa$. Known examples of uncountably categorical such structures are closely related to Hilbert space. After the speaker called attention to this phenomenon, Shelah and Usvyatsov investigated it and proved a remarkable result: if $M$ is a nonseparable Banach space structure (with countable signature) whose theory is uncountably categorical, then $M$ is prime over a Morley sequence that is an orthonormal Hilbert basis of length equal to the density of $M$. There is a wide gap between this result and verified examples of uncountably categorical Banach spaces, which leads to the question: can a stronger such result be proved, in which the connection to Hilbert space structure is clearly expressed in the geometric language of functional analysis? The main part of this talk will focus on some new examples of uncountably categorical Banach spaces that the speaker has studied. This is based on joint work with Yves Raynaud.

Differential Geometry
2:00 pm   in 243 Altgeld Hall,  Tuesday, February 21, 2012
 Del Edit Copy
Submitted by palbin.
 Frédéric Rochon (Université du Québec à Montréal)Asymptotics of the Ricci flow on quasi projective varietiesAbstract: PLEASE NOTE THE TIME CHANGE TO 2 PM! After a brief review on the Kahler-Ricci flow, we will consider Kahler metrics on quasiprojective varieties with a certain asymptotic behavior at infinity and show that this behavior is preserved as the metrics evolve according to the Kahler-Ricci flow. A key ingredient in our approach will be to compactify quasiprojective varieties by manifolds with corners. Time permitting, we will also discuss what happens to the limiting Kahler-Einstein metric when the flow converges. This is a joint work with Zhou Zhang.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 21, 2012
 Del Edit Copy
Submitted by west.
 Jozef Skokan (London School of Economics)Monochromatic cycles in 2-edge-colored graphsAbstract: The Ramsey number $r(H)$ of a graph $H$ is the smallest integer $n$ such that every 2-coloring of the edges of the complete graph on $n$ vertices contains a monochromatic copy of $H$. Schelp conjectured that if $H$ is a path or a cycle and $G$ is any graph on $r(H)$ vertices with minimum degree larger than $3r(H)/4$, then every 2-coloring of the edges of $G$ contains a monochromatic copy of $H$. In this talk, we shall discuss the ideas in our proof of the conjecture for long paths and cycles. (Joint work with B. Bollobas, F. Benevides, T. Luczak, A. Scott, and M. White.)

Wednesday, February 22, 2012

Study Seminar in Geometry and Analysis
3:00 pm   in 347 Altgeld Hall,  Wednesday, February 22, 2012
 Del Edit Copy
Submitted by jathreya.
 Jayadev Athreya (UIUC)Volume growth entropy decreases along Ricci FlowAbstract: We will sketch Manning's proof that the volume growth entropy for a Riemannian metric on a compact genus $g$ surface decreases along Ricci flow, modulo some black boxes. We will discuss some open problems and make some unfounded speculation.

Thursday, February 23, 2012

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 23, 2012
 Del Edit Copy
Submitted by kapovich.
 Nathan Dunfield (UIUC Math)Integer homology 3-spheres with large injectivity radiusAbstract: Conjecturally, the amount of torsion in the first homology group of a hyperbolic 3-manifold must grow rapidly in any exhaustive tower of covers (see Bergeron-Venkatesh and F. Calegari-Venkatesh). In contrast, the first betti number can stay constant (and zero) in such covers. Here "exhaustive" means that the injectivity radius of the covers goes to infinity. In this talk, I will explain how to construct hyperbolic 3-manifolds with trivial first homology where the injectivity radius is big almost everywhere by using ideas from Kleinian groups. I will then relate this to the recent work of Abert, Bergeron, Biringer, et. al. In particular, these examples show a differing approximation behavior for L^2 torsion as compared to L^2 betti numbers. This is joint work with Jeff Brock.

2:00 pm   in 241 Altgeld Hall,  Thursday, February 23, 2012
 Del Edit Copy
Submitted by lukyane2.
 Brian Collier (UIUC Math)Motivating Hamiltonian Floer TheoryAbstract: The focus of this talk will be to motivate the main ideas in Hamiltonian Floer theory. To start, we will review the notion of a Hamiltonian vector field and other important things in symplectic geometry. We will then talk about Morse Theory in a manner that will generalize most naturally to the infinite dimensional situation. Finally I will introduce Hamiltonian Floer Theory as the analog of the Morse theory of a certain action functional.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 23, 2012
 Del Edit Copy
Submitted by kapovich.
 Amie Wilkinson (University of Chicago)Absolute continuity, exponents, and rigidityAbstract: The geodesics in a compact surface of negative curvature display stability properties originating in the chaotic, hyperbolic nature of the geodesic flow on the associated unit tangent bundle. Considered as a foliation of this bundle, this collection of geodesics persists in a strong way when one perturbs of the Riemannian metric, or the geodesic flow generated by this metric, or even the time-one map of this flow: for any perturbed system there is a corresponding "shadow foliation" with one-dimensional smooth leaves that is homeomorphic to the original geodesic foliation. A counterpart to this foliation stability is a curious rigidity phenomenon that arises when one studies the disintegration of volume along the leaves of this perturbed shadow foliation. I will describe this phenomenon and its underlying causes. This is recent work with Artur Avila and Marcelo Viana.

Friday, February 24, 2012

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, February 24, 2012
 Del Edit Copy
Submitted by phierony.
 Slawomir Solecki (UIUC)The pseudo-arc and its homeomorphism groupAbstract: The pseudo-arc can be constructed as a natural quotient of a projective Fraisse limit P. I will outline this construction and indicate its possible connections with random walk. I will prove an anti-Ramsey theorem (i.e., find an appropriate coloring) for a certain type of structures, which will show, via a dualization of the Kechris--Pestov--Todorcevic theory, that the group of automorphisms of P fixing a given point is not extremely amenable. The theme above will be continued in the next two talks by Ola Kwiatkowska on the work of Oppenheim.

Tuesday, February 28, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, February 28, 2012
 Del Edit Copy
Submitted by jathreya.
 Francois Ledrappier (Notre Dame)Entropy rigidity for non-positively curved compact manifolds.Abstract: We consider different asymptotic rates related to the geometry of the universal cover of a compact manifold. We discuss relations between these rates, a characterization of symmetric spaces of non-positive curvature and related problems.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, February 28, 2012
 Del Edit Copy
Submitted by franklan.
 Paul Goerss (Northwestern University)Brown-Comenetz duality in the K(2)-local categoryAbstract: The principal result I will discuss is the identification of the homotopy type of the Brown-Comenetz dual of the K(2)-local sphere at p=3. Given the rather technical nature of this computation, I will probably spend more time on why this is an interesting question than on techniques of proof.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, February 28, 2012
 Del Edit Copy
Submitted by berdogan.
 Andrew Lawrie (U Chicago Math)Scattering for wave maps exterior to a ballAbstract: In this talk I will discuss some recent work that was completed in collaboration with Professor Wilhelm Schlag. We consider $1$-equivariant wave maps from $\mathbb{R}_t\times (\mathbb{R}^3_x\setminus B) \to S^3$ where $B$ is a ball centered at $0$, and $\partial B$ gets mapped to a fixed point on~$S^3$. We show that $1$-equivariant maps of degree zero scatter to zero irrespective of their energy. For positive degrees, we prove asymptotic stability of the unique harmonic maps in the energy class determined by the degree.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 28, 2012
 Del Edit Copy
Submitted by ssolecki.
 Slawomir Solecki (Department of Mathematics, University of Illinois at Urbana-Champaign)Point realizations of Boolean actionsAbstract: I will show that if $M$ is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from $M$ to $U(1)$ on a separable probability algebra which preserves the measure and yet does not admit a point realization in the sense of Mackey. This is in contrast with Mackey's point realization theorem for locally compact, second countable groups. The proof of the above theorem goes through showing certain results concerning the infinite dimensional Gaussian measure space $({\mathbb C}^{\mathbb N},\gamma_\infty)$ which contrasts the Cameron--Martin Theorem. I will place the main result in the background of recent work on point realization and lack thereof for various classes of Polish groups. These results are due to Becker, Glasner, Tsirelson, Weiss, Kwiatkowska and myself. This is a joint work with Justin Moore.

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, February 28, 2012
 Del Edit Copy
Submitted by kkirkpat.
 Scott Armstrong   [email] (U Wisconsin Math)Random homogenization of Hamilton-Jacobi equationsAbstract: I will describe some recent work with Souganidis on the stochastic homogenization of Hamilton-Jacobi equations (both "viscous" as well as first-order equations). The homogenization of special cases of these equations has a direct connection to the work of Sznitman on the quenched large deviations of Brownian motion in the presence of Poissonian obstacles. It also benefits from some strong analogies to certain aspects of the theory of first-passage percolation.

Graph Theory and Combinatorics
3:00 pm   in Altgeld Hall,  Tuesday, February 28, 2012
 Del Edit Copy
Submitted by west.
 Alexandr Kostochka (Department of Mathematics, University of Illinois at Urbana-Champaign)Ks,t-minors in dense graphs and in (s+t)-chromatic graphsAbstract: We refine two known results on the existence of $K_{s,t}$-minors in graphs. First we prove that if $(t/\log_2 t)\ge 1000s$, then every graph $G$ with average degree at least $t+8s\log_2 s$ has a $K^*_{s,t}$-minor, where $K^*_{s,t}$ is the graph obtained from $K_{s,t}$ by adding the edges of a complete graph on the first partite set. This result refines a result by Kühn and Osthus and is joint work with N. Prince. It was proved earlier that for sufficiently large $t$ in terms of $s$, every graph with chromatic number $s+t$ has a $K^*_{s,t}$-minor. In particular, with $t_0(s) = \max\{4^{15s^2+s},(240s\log_2{s})^{8s\log_2{s}+1}\}$, the conclusion holds when $t>t_0(s)$. This result confirmed a special case of a conjecture by Woodall and Seymour. We show that the conclusion holds already for much smaller $t$, namely, for $t>C(s\log s)^3$.

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Tuesday, February 28, 2012
 Del Edit Copy
Submitted by kapovich.
 Rui Loja Fernandes (Instituto Superior Tecnico, Portugal)Stability of LeavesAbstract: I will start by recalling some classical results on stability of periodic orbits of flows (Poincaré), of leaves of foliations (Reeb-Thurston), and of orbits of group actions (Hirsch-Stowe). Then I will explain a new result on stability of symplectic leaves in Poisson geometry (joint work with M. Crainic) and how all these apparent distinct results can be related using Lie groupoid theory. Time permitting, I will state a related conjecture in KAM theory.

Wednesday, February 29, 2012

Study Seminar in Geometry and Analysis
3:00 pm   in 345 Altgeld Hall,  Wednesday, February 29, 2012
 Del Edit Copy
Submitted by palbin.
 Pierre Albin   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Compactness of isospectral manifoldsAbstract: We will commence our study of the Osgood-Phillips-Sarnak papers on the compactness of isospectral surfaces. I will discuss compactness of isospectral sets of manifolds with a curvature bound. In a follow-up talk I will discuss the case of surfaces.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, February 29, 2012
 Del Edit Copy
Submitted by katz.
 Sheldon Katz   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Introduction to Algebraic GeometryAbstract: Illustrating throughout with plane curves, I will give a tour of algebraic geometry, touching on both the classical and the modern. I will also give connections to other areas of study, from elementary calculus to string theory in theoretical physics.

Thursday, March 1, 2012

Number Theory Seminar
11:00 am   in 243 Altgeld Hall,  Thursday, March 1, 2012
 Del Edit Copy
Submitted by ford.
 Xiannan Li (Department of Mathematics, University of Illinois at Urbana-Champaign)The least prime that does not split in a number fieldAbstract: I will begin by describing some classical work on unconditionally bounding the least quadratic non-residue dating back to Vinogradov and Burgess. A generalization of this problem is to bound the least prime that does not split completely in a number field, which was studied by K. Murty and then by Vaaler and Voloch. I will describe two different approaches, one based on zeros of L-functions, and the other on the theory of multiplicative functions, which give the best known bounds here when the degree of the number field is larger than 2.

Group Theory Seminar
1:00 pm   in 347 Altgeld Hall,  Thursday, March 1, 2012
 Del Edit Copy
Submitted by dsrobins.
 Derek Robinson (Department of Mathematics, University of Illinois at Urbana-Champaign)Groups with few isomorphism types of derived subgroup.Abstract: A derived subgroup in a group G is the derived (or commutator) subgroup of some subgroup of G. Recently there has been interest in trying to understand the significance of the set of derived subgroups within the lattice of all subgroups of G. In particular one can ask about the effect on the group structure of imposing restrictions on the set of derived subgroups. In this talk we will describe recent work on groups in which there are at most two isomorphism types of derived subgroup. While this may sound like a very special class of groups, it contains groups of many diverse types. We will describe some of these types of group and show how their construction involves some interesting number theoretic problems.

2:00 pm   in 241 Altgeld Hall,  Thursday, March 1, 2012
 Del Edit Copy
Submitted by lukyane2.
 Juan Villeta-Garcia (Department of Mathematics, University of Illinois at Urbana-Champaign)The Harder-Narasimhan stratification of quiver representationsAbstract: A quiver is a finite graph with orientations, and their representations are defined by assigning vector spaces to each vertex and linear maps to each arrow. The theory of quiver representations is incredibly broad, with applications to such areas as quantum physics, Lie theory and invariant theory. We will give a brief overview of the category of quiver representations, and use a construction of Reineke that mimics the Harder-Narasimhan filtration for vector bundles, to analyze this category.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, March 1, 2012
 Del Edit Copy
Submitted by kapovich.
 Daniel Král' (Charles University, Czech Republic)Testing first order logic properties in sparse combinatorial structuresAbstract: Algorithmic metatheorems guarantee that certain types of problems have efficient algorithms. A classical example is the theorem of Courcelle asserting that every monadic second-order logic (MSOL) property can be tested in linear time for graphs with bounded tree-width. As examples of MSOL properties let us mention 3-colorability, hamiltonicity, etc., all well-known NP-hard problems. In this talk, we focus on simpler properties, those that can be expressed in first order logic (FOL). An example of FOL property is an existence of a fixed substructure. While it is not hard to show that every FOL property can be decided in polynomial time, our desire is to design algorithms with faster running time (e.g. linear time). We recall a recent notion of graph classes with bounded expansion, which include classes of graphs with bounded maximum degree and proper-minor closed classes of graphs. We then apply structural results to show that FOL properties can be tested in linear time for classes of graphs with bounded expansion and we will discuss extensions to other structures. At the end of the talk, we will mention several open problems as well as directions for future research. This talk is based on joint work with Zdenek Dvorák and Robin Thomas.

5:00 pm   in 147 Altgeld Hall,  Thursday, March 1, 2012
 Del Edit Copy
Submitted by funk3.
 Kelly Funk (Department of Mathematics, University of Illinois at Urbana-Champaign)Rigidity Across DynamicsAbstract: We will discuss examples of rigidity and uniform rigidity sequences in ergodic theory. We will also discuss the problem of characterizing these sequences.

Tuesday, March 6, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, March 6, 2012
 Del Edit Copy
Submitted by jathreya.
 Ilya Gekhtman (University of Chicago)Dynamics of Convex Cocompact Subgroups of Mapping Class GroupsAbstract: Convex cocompact subgroups of mapping class groups are subgroups of the mapping class group whose orbits in Teichmueller space are quasi-convex. We develop an analogue of Patterson-Sullivan theory for the action of subgroups G of Mod(S) on Teichmuller space and its boundary the space of projective measured foliations and use it to compute multiplicative asymptotics for the number of orbit points of G in a ball of radius R in Teichmueller space and the number of pseudo-Anosovs in G with dilatation at most R.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, March 6, 2012
 Del Edit Copy
Submitted by franklan.
 Ayelet Lindenstrauss (Indiana University)K-theory of formal power seriesAbstract: (Joint with Randy McCarthy.) We study the algebraic K-theory of parametrized endomorphisms of a unital ring R with coefficients in a simplicial R-bimodule M, and compare it with the algebraic K-theory of the ring of formal power series in M over R. Waldhausen defined an equivalence from the suspension of the reduced Nil K-theory of R with coefficients in M to the reduced algebraic K-theory of the tensor algebra TR(M). Extending Waldhausen's map from nilpotent endomorphisms to all endomorphisms, our map has to land in the ring of formal power series rather than in the tensor algebra, and is no longer in general an equivalence (it is an equivalence when the bimodule M is connected). Nevertheless, the map shows a close connection between its source and its target: it induces an equivalence on the Goodwillie Taylor towers of the two (as functors of M, with R fixed), and allows us to give a formula for the suspension of the invariant W(R;M) (which can be thought of as Witt vectors with coefficients in M, and is what the Goodwillie Taylor tower of the source functor converges to) as the inverse limit, as n goes to infinity, of the reduced algebraic K-theory of TR(M)/ (Mn).

Harmonic analysis and differential equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, March 6, 2012
 Del Edit Copy
Submitted by vzh.
 Taras Lakoba, (University of Vermont, Math)Unusual properties of numerical instability of the split-step method applied to NLS solitonAbstract: The split-step method (SSM) is widely used for numerical solution of nonlinear evolution equations. Its idea and implementation are simple. Namely, it is common that the evolution of variable $u$ is governed by: $u_t = A(u,t) + B(u,t)$ where both individual'' evolutions $u_t = A(u,t) \qquad \mbox{and} \qquad u_t = B(u,t)$ can be solved exactly (or at least easily''). Then the numerical approximation of the full solution is sought in steps that alternatingly solve each equation. The SSM has long been used to simulate the NLS: $$i \, u_t - \beta u_{xx} + \gamma u|u|^2 = 0$$ ( so here $A=-\beta u_{xx}$ and $B=\gamma u|u|^2$). However, until recently, a possible development of numerical instability of the SSM has been studied only in one simplest case, which does not include the soliton or multi-soliton solutions of the NLS. In this talk I will present recent results concerning the development of the numerical instability of the SSM when it is used to simulated a near-soliton solution of NLS. Properties of this instability are stunningly different from instability properties of most other numerical schemes. I will not assume prior familiarity of the audience with instabilities of numerical methods and therefore will first review a couple of basic examples of such instabilities. This will set a benchmark for the subsequent exposition of the instability properties of the SSM. I will show how those properties, and --- more importantly --- their analysis, are different from the instability properties and analysis for most other numerical schemes.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 6, 2012
 Del Edit Copy
Submitted by ssolecki.
 Lou van den Dries (Department of Mathematics, University of Illinois at Urbana-Champaign)The structure of approximate groups according to Breuillard, Green, TaoAbstract: Roughly speaking, an approximate group is a finite symmetric subset A of a group such that AA can be covered by a small number of left-translates of A. Last year the authors mentioned in the title established a conjecture of H. Helfgott and E. Lindenstrauss to the effect that approximate groups are finite-by-nilpotent''. This may be viewed as a sweeping generalisation of both the Freiman-Ruzsa theorem on sets of small doubling in the additive group of integers, and of Gromov's characterization of groups of polynomial growth. Among the applications of the main result are a finitary refinement of Gromov's theorem and a generalized Margulis lemma conjectured by Gromov. Prior work by Hrushovski on approximate groups is fundamental in the approach taken by the authors. They were able to reduce the role of logic to elementary arguments with ultra products. The point is that an ultraproduct of approximate groups can be modeled in a useful way by a neighborhood of the identity in a Lie group. This allows arguments by induction on the dimension of the Lie group. I will give two talks: the one on Tuesday will describe the main results, and the sequel on Friday will try to give a rough idea of the proofs.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, March 6, 2012
 Del Edit Copy
Submitted by kkirkpat.
 Jonathon Peterson   [email] (Purdue)Large deviations and slowdown asymptotics for excited random walksAbstract: Excited random walks (also called cookie random walks) are self-interacting random walks where the transition probabilities depend on the number of previous visits to the current location. Although the models are quite different, many of the known results for one-dimensional excited random walks have turned out to be remarkably similar to the corresponding results for random walks in random environments. For instance, one can have transience with sub-linear speed and limiting distributions that are non-Gaussian. In this talk I will prove a large deviation principle for excited random walks. The main tool used will be what is known as the "backwards branching process" associated with the excited random walk, thus reducing the problem to proving a large deviation principle for the empirical mean of a Markov chain (a much simpler task). While we do not obtain an explicit formula for the large deviation rate function, we will be able to give a good qualitative description of the rate function. While many features of the rate function are similar to the corresponding rate function for RWRE, there are some interesting differences that highlight the major difference between RWRE and excited random walks.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 6, 2012
 Del Edit Copy
Submitted by west.
 Andrew Treglown (Charles University, Prague)Embedding spanning bipartite graphs of small bandwidthAbstract: A graph $H$ on $n$ vertices has bandwidth at most $b$ if there exists a labelling of the vertices of $H$ by the numbers $1,\ldots,n$ such that $|i-j|\le b$ for every edge $ij$ of $H$. Boettcher, Schacht, and Taraz gave a condition on the minimum degree of a graph $G$ on $n$ vertices to ensure that $G$ contains every $r$-chromatic graph $H$ on $n$ vertices having bounded degree and bandwidth $o(n)$, thereby proving a conjecture of Bollobás and Komlós. We strengthen this result in the case where $H$ is bipartite. Indeed, we give an essentially best-possible condition on the degree sequence of a graph $G$ on $n$ vertices that forces $G$ to contain every bipartite graph $H$ on $n$ vertices having bounded degree and bandwidth $o(n)$. This also implies an Ore-type result. In fact, we prove a much stronger result where the condition on $G$ is relaxed to a certain robust expansion property. (Joint work with Fiachra Knox.)

Mathematical Biology
3:00 pm   in 345 Altgeld Hall,  Tuesday, March 6, 2012
 Del Edit Copy
Submitted by zrapti.
 Spencer Hall   [email] (Indiana University, Department of Biology )Five reasons why resources matter for diseaseAbstract: We could produce more powerful theory to predict disease outbreaks if we took an approach rooted in community ecology. I want to argue this point by focusing on resources of hosts and a case study of fungal disease in a planktonic grazer (Daphnia). Using this system and a combination of observations of epidemics in lakes, experiments, and mathematical (differential equation) models, I will show five reasons why resources matter for disease. (1) Key epidemiological traits (think transmission rate, or yield of parasites from infected host) vary plastically with resources - and how hosts acquire and use them. (2) If we embrace this plasticity, we can better predict variation in disease in time and space. I'll illustrate with a case study of potassium as the resource. A model will also reveal some counter-intuitive predictions that stem from interactions of disease with a dynamic resource. (3) Resources can strongly influence how other species (predators, competitors) inhibit or fuel epidemics. For example, I'll show how a predator might spread disease through a trophic cascade. (4) Variation in feeding rate (i.e., resource acquisition) among clonal genotypes of hosts can create key tradeoffs in life history vs. epidemiological traits (e.g., transmission rate vs. fecundity). (5) This tradeoff can then help us understand how hosts might evolve to become more resistant or more susceptible to their parasites during epidemics of different sizes. All of these ecological and evolutionary outcomes for disease hinge on explicitly thinking about resources of hosts. As a result, host-resource interactions should play a much more prominent role in rapidly growing theory for disease ecology.

Mathematics Colloquium --Trjitzinsky Memorial Lectures
4:00 pm   in 314 Altgeld Hall,  Tuesday, March 6, 2012
 Del Edit Copy
Submitted by kapovich.
 Robert Ghrist (University of Pennsylvania)Sheaves and the Global Topology of Data, Lecture IAbstract: This lecture series concerns Applied Mathematics -- the taming and tuning of mathematical structures to the service of problems in the sciences. The Mathematics to be harnessed comes from algebraic topology -- specifically, sheaf theory, the study of local-to-global data. The applications to be surveyed are in the engineering sciences, but are not fundamentally restricted to such. Beginning with a gentle introduction to algebraic topology and its modern applications, the series will focus on sheaves and their recent utility in sensing, coding, optimization, and inference. No prior exposure to sheaves required. Robert Ghrist is the Andrea Mitchell Penn Integrating Knowledge Professor in the Departments of Mathematics and Electrical/Systems Engineering at the University of Pennsylvania. A reception will be held in AH 314 immediately following the lecture.

Wednesday, March 7, 2012

GEAR Brown Bag
12:00 pm   in 331 Altgeld Hall,  Wednesday, March 7, 2012
 Del Edit Copy
 To Be AnnouncedAbstract: Bring your lunch and join us for informal discussion of all matters relating to GEometric structures And Representation varieties. GEAR will provide cookies.

Mathematics Colloquium --Trjitzinsky Memorial Lectures
4:00 pm   in 245 Altgeld Hall,  Wednesday, March 7, 2012
 Del Edit Copy
Submitted by kapovich.
 Robert Ghrist (University of Pennsylvania)Sheaves and the Global Topology of Data, Lecture IIAbstract: This lecture series concerns Applied Mathematics -- the taming and tuning of mathematical structures to the service of problems in the sciences. The Mathematics to be harnessed comes from algebraic topology -- specifically, sheaf theory, the study of local-to-global data. The applications to be surveyed are in the engineering sciences, but are not fundamentally restricted to such. Beginning with a gentle introduction to algebraic topology and its modern applications, the series will focus on sheaves and their recent utility in sensing, coding, optimization, and inference. No prior exposure to sheaves required.

Thursday, March 8, 2012

Joint Group Theory/Differential Geometry/Ergodic Theory
1:00 pm   in 347 Altgeld Hall,  Thursday, March 8, 2012
 Del Edit Copy
Submitted by jathreya.
 Alex Wright (University of Chicago)Arithmetic and Non-Arithmetic Teichmüller CurvesAbstract: Teichmüller curves are isometrically immersed curves in the moduli space of Riemann surfaces. Their study lies at the intersection of dynamics, Teichmüller theory, and algebraic geometry. I will begin by summarizing known results on Teichmüller curves, pointing out some similarities to the study of lattices, for example in PU(n,1). I will then move on to new research involving abelian square-tiled surfaces, Schwarz triangle mappings, and the Veech-Ward-Bouw-Moller Teichmüller curves.

2:00 pm   in 241 Altgeld Hall,  Thursday, March 8, 2012
 Del Edit Copy
Submitted by lukyane2.
 Sarah Yeakel (Department of Mathematics, University of Illinois at Urbana-Champaign)SpectraAbstract: I'll define spectra with motivation from homotopy theory, explain why they form a nicer category than topological spaces, and talk about how they are useful tools in pretty much any setting with a (co)homology theory.

Mathematics Colloquium --Trjitzinsky Memorial Lectures
4:00 pm   in 245 Altgeld Hall,  Thursday, March 8, 2012
 Del Edit Copy
Submitted by kapovich.
 Robert Ghrist (University of Pennsylvania)Sheaves and the Global Topology of Data, Lecture IIIAbstract: This lecture series concerns Applied Mathematics -- the taming and tuning of mathematical structures to the service of problems in the sciences. The Mathematics to be harnessed comes from algebraic topology -- specifically, sheaf theory, the study of local-to-global data. The applications to be surveyed are in the engineering sciences, but are not fundamentally restricted to such. Beginning with a gentle introduction to algebraic topology and its modern applications, the series will focus on sheaves and their recent utility in sensing, coding, optimization, and inference. No prior exposure to sheaves required.

Friday, March 9, 2012

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, March 9, 2012
 Del Edit Copy
Submitted by phierony.
 Lou van den Dries (Department of Mathematics, University of Illinois at Urbana-Champaign)The structure of approximate groups according to Breuillard, Green, Tao.Abstract: Roughly speaking, an approximate group is a finite symmetric subset A of a group such that AA can be covered by a small number of left-translates of A. Last year the authors mentioned in the title established a conjecture of H. Helfgott and E. Lindenstrauss to the effect that approximate groups are finite-by-nilpotent''. This may be viewed as a sweeping generalisation of both the Freiman-Ruzsa theorem on sets of small doubling in the additive group of integers, and of Gromov's characterization of groups of polynomial growth. Among the applications of the main result are a finitary refinement of Gromov's theorem and a generalized Margulis lemma conjectured by Gromov. Prior work by Hrushovski on approximate groups is fundamental in the approach taken by the authors. They were able to reduce the role of logic to elementary arguments with ultra products. The point is that an ultraproduct of approximate groups can be modeled in a useful way by a neighborhood of the identity in a Lie group. This allows arguments by induction on the dimension of the Lie group. I will give two talks: the one on Tuesday (1pm in 345 AH) will describe the main results, and the sequel on Friday (4pm in 347 AH) will try to give a rough idea of the proofs.

Monday, March 12, 2012

Mathematics Colloquium - Special Lecture 2011-12
1:00 pm   in 143 Altgeld Hall,  Monday, March 12, 2012
 Del Edit Copy
Submitted by kapovich.
 Amit Singer (Princeton)Vector Diffusion Maps and the Connection LaplacianAbstract: Motivated by problems in structural biology, specifically cryo-electron microscopy, we introduce vector diffusion maps (VDM), a new mathematical framework for organizing and analyzing high dimensional data sets, 2D images and 3D shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and other non-linear dimensionality reduction methods, such as LLE, ISOMAP and Laplacian eigenmaps. While existing methods are either directly or indirectly related to the heat kernel for functions over the data, VDM is based on the heat kernel for vector fields. VDM provides tools for organizing complex data sets, embedding them in a low dimensional space and interpolating and regressing vector fields over the data. In particular, it equips the data with a metric, which we refer to as the vector diffusion distance. In the manifold learning setup, where the data set is distributed on a low dimensional manifold Md embedded in Rp, we prove the relationship between VDM and the connection-Laplacian operator for vector fields over the manifold. Applications to structural biology (cryo-electron microscopy and NMR spectroscopy), computer vision and shape space analysis will be discussed. (Joint work with Hau-tieng Wu.)

Tuesday, March 13, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, March 13, 2012
 Del Edit Copy
Submitted by franklan.
 Gabriel Drummond-Cole (Northwestern University)Homotopically trivializing the circle in the framed little disksAbstract: An action of the space of framed little disks on a target space induces a circle action on the target space. Kontsevich suggested that an action of the framed little disks along with a trivialization of the circle action could be encapsulated as follows: this data should be the same as an action of the Deligne-Mumford-Knudsen compactified genus zero moduli space. I'll present a rigorous formulation of this statement in the category of topological operads. There will be many pictures.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, March 13, 2012
 Del Edit Copy
Submitted by ekirr.
 Christof Sparber (UIC Math)High frequency interactions in nonlinear Schroedinger equations and applicationsAbstract: We consider the cubic nonlinear Schroedinger equation in a weakly nonlinear semiclassical scaling and analyze the interaction of highly oscillatory waves within this context. An extension to the Davey-Stewartson system will be discussed, as well as applications in proving ill-posedness of NLS in Sobolev spaces of negative order. This is based joint works with R. Carles and E. Dumas.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 13, 2012
 Del Edit Copy
Submitted by ssolecki.
 Christian Rosendal (UIC)Global and local boundedness of Polish groupsAbstract: We present a comprehensive theory of boundedness properties for Polish groups developed with a main focus on Roelcke precompactness (precompactness of the lower uniformity) and Property (OB) (boundedness of all isometric actions on separable metric spaces). In particular, these properties are characterised by the orbit structure of isometric or continuous affine representations on separable Banach spaces or Hilbert space.

Geometry Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, March 13, 2012
 Del Edit Copy
Submitted by sba.
 Stephanie Alexander (Department of Mathematics, University of Illinois at Urbana-Champaign)The unit sphere in flat space-time, anti-deSitter space, and modeling particle interactions.Abstract: We introduce the geometry of the unit spheres'' in the flat space-time $\mathbf{R^4_-}$, as well as in $\mathbf{R^4_{--}}$. These unit spheres may be called hyperbolic - de Sitter space'' and $\pm$ anti-deSitter space''. We explain how these spaces, and a realization theorem of Schlenker on convex surfaces, are used to model particle interactions. This is an expository talk, emphasizing visualization.

Algebraic Geometry
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 13, 2012
 Del Edit Copy
Submitted by schenck.
 Tom Nevins   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Derived equivalence of quantum symplectic varietiesAbstract: Singular symplectic varieties and their resolutions of singularities lie at the crossroads of algebraic and symplectic geometry, representation theory, and integrable systems. Central examples include the nilpotent cone of a complex semisimple Lie algebra and its resolution by the cotangent bundle of the flag variety (the Springer resolution); the nth symmetric product of the affine plane and its resolution by the Hilbert scheme of points; and a Kleinian surface singularity and its minimal resolution. A singular variety and its resolution never have equivalent geometry (as encoded, for example, in their derived categories). Replacing a symplectic variety by a quantization, however---an algebro-geometric analog of passing to a Fukaya-type category---one miraculously finds that such equivalences are common. I'll discuss singular symplectic varieties and their resolutions, examples, quantization, and a general criterion for such geometric equivalences that extends classical results (for example, Beilinson-Bernstein localization). Time permitting, I'll also discuss some additional features of these quantizations that parallel emerging structures in the (much more complicated) world of Fukaya categories. This is based on joint work with K. McGerty.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 13, 2012
 Del Edit Copy
Submitted by west.
 Jeffrey Paul Wheeler (University of Pittsburgh)The Polynomial Method of Alon, Ruzsa, and NathansonAbstract: We will explore a particular method of tackling problems in Additive Combinatorics, namely the Polynomial Method of Noga Alon, Imre Ruzsa, and Melvyn Nathanson.  Additive Combinatorics can be described as the study of additive structures of sets.   This area is attractive in that it has numerous connections with other areas of mathematics, including Number Theory, Ergodic Theory, Graph Theory, Finite Geometry, and Group Theory and has drawn the attention of many good mathematicians, including Fields Medalist Terence Tao (2006).

Wednesday, March 14, 2012

GEAR Brown Bag
12:00 pm   in 331 Altgeld Hall,  Wednesday, March 14, 2012
 Del Edit Copy
 To Be AnnouncedAbstract: Bring your lunch and join us for informal discussion of all matters relating to GEometric structures And Representation varieties. This week we'll start off talking about quadratic differentials and Higgs bundles and see where that takes us. GEAR will provide cookies.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, March 14, 2012
 Del Edit Copy
Submitted by seminar.
 Maarten Bergvelt (Department of Mathematics, University of Illinois at Urbana-Champaign)Integrable Systems and Cluster AlgebrasAbstract: Integrable system occur in many areas of mathematics (and physics). I will give an overview, ending with a brief discussion of the (still obscure) relation with cluster algebras.

Thursday, March 15, 2012

Joint number theory / algebraic geometry seminar
11:00 am   in 217 Noyes,  Thursday, March 15, 2012
 Del Edit Copy
Submitted by ford.
 Noam Elkies (Harvard Math)On the areas of rational trianglesAbstract: By a "rational triangle" we mean a plane triangle whose sides are rational numbers. By Heron's formula, there exists such a triangle of area $\sqrt{a}$ if and only if $a > 0$ and $x y z (x + y + z) = a$ for some rationals $x, y, z$. In a 1749 letter to Goldbach, Euler constructed infinitely many such $(x, y, z)$ for any rational $a$ (positive or not), remarking that it cost him much effort, but not explaining his method. We suggest one approach, using only tools available to Euler, that he might have taken, and use this approach to construct several other infinite families of solutions. We then reconsider the problem as a question in arithmetic geometry: $xyz(x+y+z) = a$ gives a K3 surface, and each family of solutions is a singular rational curve on that surface defined over $\mathbb{Q}$. The structure of the Neron-Severi group of that K3 surface explains why the problem is unusually hard. Along the way we also encounter the Niemeier lattices (the even unimodular lattices in $\mathbb{R}^{24}$) and the non-Hamiltonian Petersen graph.

Harmonic Analysis and Differential Equations
1:00 pm   in 345 Altgeld Hall,  Thursday, March 15, 2012
 Del Edit Copy
Submitted by ekirr.
 Irina Nenciu (UIC Math)Essential self-adjointness criteria for Schroedinger operators on bounded domainsAbstract: We consider a Schroedinger operator on a bounded domain in R^n, and search for optimal growth criteria for the potential close to the boundary of the domain insuring essential self-adjointness of the associated operator. We find an abstract integral criterion for the potential, from which we prove that one can add optimal logarithmic type corrections to the classical criteria. As a consequence of our method, we study the question of confinement of spinless and spin 1/2 quantum particles on the unit disk in R^2, and achieve magnetic confinement solely by means of the growth of the magnetic field.

2:00 pm   in 241 Altgeld Hall,  Thursday, March 15, 2012
 Del Edit Copy
Submitted by lukyane2.
 Peter Nelson (Department of Mathematics, University of Illinois at Urbana-Champaign)Formal groups in algebraic topologyAbstract: Formal groups are objects that lie between Lie groups and Lie algebras. I'll motivate their application to geometry and topology by discussing Chern classes of vector bundles. Then I'll talk about their role in algebraic topology. This theory provides a deep connection between topology and algebraic geometry and even number theory.

Mathematics in Science and Society (MSS)
4:00 pm   in Great Hall, Krannert Center for the Performing Arts,  Thursday, March 15, 2012
 Del Edit Copy
Submitted by kapovich.
 Noam Elkies (Harvard University)Canonical forms: A mathematician's view of musical canonsAbstract: To write a musical canon -- be it "Three Blind Mice" or the climax of a Bach fugue -- one constructs a melody that can act as its own harmony. Thinking about this task leads us to look at musical structure from points of view usually associated with science and mathematics, not the arts. The lecture will be illustrated with diagrams as well as musical examples form various eras and genres (including at least one improvised on the spot), and will require no technical background in either music or mathematics.

Friday, March 16, 2012

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, March 16, 2012
 Del Edit Copy
Submitted by phierony.
 Aleksandra Kwiatkowska (Department of Mathematics, University of Illinois at Urbana-Champaign)The pseudo-arc and its homeomorphism group, part 2Abstract: Continuing the talk by Slawomir Solecki on February 24, we further explore properties of the pseudo-arc and of its homeomorphism group. We plan to talk around the work of Oppenheim on the problem of the existence of a dense conjugacy class in the group of all homeomorphisms of the pseudo-arc. The projective Fraisse theory plays a crucial role in his work.

Tuesday, March 27, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, March 27, 2012
 Del Edit Copy
Submitted by jathreya.
 Anish Ghosh (University of East Anglia)Measure Rigidity for torus actionsAbstract: Recent years have seen major developments in the theory of measure rigidity for group actions on homogeneous spaces. I will explain some of these developments and present a few recent advances.

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, March 27, 2012
 Del Edit Copy
Submitted by ford.
 Vorrapan Chandee (CRM, University of Montreal)Bounding S(t) via extremal functionsAbstract: Assuming the Riemann hypothesis we consider the argument function of the Riemann zeta function, $S(t)$. We will prove that for large $t$, $$|S(t)| \leq ( 1/4 + o(1) ) \log t /\log \log t,$$ which is an improvement of the previous work of Goldston and Gonek by a factor of 2. The result may reasonably be thought of as having attained the limit of existing methods of bounding $S(t)$ under RH. Two different approaches to improve a bound for $S(t)$ will be presented in the talk. Both methods rely on the solution of the Beurling-Selberg extremal problem from recent works by Carneiro, Littmann and Vaaler.

Topology Seminar
11:00 am   Tuesday, March 27, 2012
 Del Edit Copy
Submitted by franklan.
 Seminar canceled today

Probability Seminar
2:00 pm   in Altgeld Hall,  Tuesday, March 27, 2012
 Del Edit Copy
Submitted by kkirkpat.
 Philip Matchett Wood (U Wisconsin-Madison)Survey of the Circular LawAbstract: What do the eigenvalues of a random matrix look like? This talk will focus on large square matrices where the entries are independent, identically distributed random variables. In the most basic case, the distribution of the eigenvalues in the complex plane (suitably scaled) approaches the uniform distribution on the unit disk, which is called the circular law. We will discuss some of the methods that have been used to prove the circular law, including recent work that has extended the circular law to the most general situation, and we will also discuss generalizations to situations where the eigenvalue distributions are stable, but non-circular.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 27, 2012
 Del Edit Copy
Submitted by west.
 Cory Palmer (UIUC Math)Turan numbers for forestsAbstract: The Turán number of a graph $H$, written $ex(n,H)$, is the maximum number of edges in a graph on $n$ vertices that does not contain $H$ as a subgraph. The Erdős-Stone-Simonovits Theorem computes $ex(n,H)$ asymptotically for graphs of chromatic number at least 3. For bipartite graphs much is still unknown. Of particular interest is the Turán number for trees (this is the Erdős-Sós conjecture). We will concentrate our attention on the Turán number of forests. Bushaw and Kettle determined the Turán number of a forest made up of copies of a path of a fixed length. We generalize their result by finding the Turán number for a forest composed of arbitrary length paths. We also determine the Turán number for a forest made up of arbitrary size stars. In both cases we characterize the extremal graphs. (Joint work with Hong Liu and Bernard Lidicky.)

Thursday, March 29, 2012

Number Theory Seminar
11:00 am   in 243 Altgeld Hall,  Thursday, March 29, 2012
 Del Edit Copy
Submitted by ford.
 Florian Luca (Univ. Morelia, Mexico)On the local behavior of the Ramanujan tau functionAbstract: Let $\tau(n)$ be the Ramanujan function given by $$\sum_{n\ge 1} \tau(n) q^n = q\prod_{i\ge 1} (1-q^i)^{24}.$$ Lehmer conjectured that  $\tau(n)\ne 0$ for all n, and this conjecture has been verified for all $n \le 22798241520242687999$: In my talk, I will present the main ideas of the following theorem obtained jointly with Yuri Bilu (Bordeaux): If $k$ is a positive integer such that $\tau(m) \ne 0$ for all $m \le k$, then for every permutation $\sigma$ of the first $k$ positive integers, there exist infinitely many positive integers $n$ such that $\tau(n + \sigma(1)) < \cdots < \tau(n + \sigma(k))$: In other words, the absolute value of the Ramanujan-function may behave in all possible ways (increasing, decreasing, etc.) on intervals of length $k$ provided of course that it does not vanish with a certain periodicity inside such intervals. The proof is quite elementary in essence (Chinese Remainder Theorem) although we appeal to lower bounds for linear forms in logarithms of algebraic numbers to justify certain estimates and to sieves and the truth of the Sato-Tate conjecture for $\tau(n)$ to avoid certain primes.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, March 29, 2012
 Del Edit Copy
Submitted by kapovich.
 Matt Clay (Alleheny College)Relative twisting in Outer spaceAbstract: The Culler-Vogtmann Outer space is the space of marked metric graphs of a fixed rank. It plays a similar role in the theory of the group of outer automorphisms of a free group as the Teichmueller space of a surface plays for the mapping class group of the surface. I will discuss a tool for providing a lower bound on the distance between points in the Outer space with the Lipschitz metric that is akin to annular projection in surfaces. This is joint work with Alexandra Pettet.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, March 29, 2012
 Del Edit Copy
Submitted by aimo.
 Dean Baskin (Northwestern)Asymptotics of radiation fields in asymptotically Minkowski spaceAbstract: Radiation fields are (appropriately rescaled) limits of solutions of wave equations along light rays. In this talk I will describe a class of (non-static) asymptotically Minkowski space times for which the radiation field is defined and indicate how methods of Vasy can be used to express the asymptotics in terms of the resonances of a related Riemannian problem on an asymptotically hyperbolic manifold. In particular, even on Minkowski space, these methods give a new understanding of the Klainerman-Sobolev estimates. This is joint work with Andras Vasy and Jared Wunsch.

2:00 pm   in 241 Altgeld Hall,  Thursday, March 29, 2012
 Del Edit Copy
Submitted by lukyane2.
 Santiago Camacho (UIUC Math)Some first order definable properties of Tropical GeometryAbstract: There are many different ways one can approach tropical geometry, approximation by amoebas generated by algebraic varieties in $\mathbb{C}^n$, the valuation map over algebraic varieties of general algebraically closed valued fields, or just simply the geometry of the min-plus tropical semiring of $\mathbb{R}$. On this talk we focus on these last two and give a sketch of a proof of the fundamental theorem of tropical geometry linking them together, using elementary model theoretic tools. No previous knowledge on logic will be a assumed.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, March 29, 2012
 Del Edit Copy
Submitted by kapovich.
 James Haglund (University of Pennsylvania)Macdonald Polynomials and the Hilbert Series of the Quotient Ring of Diagonal CoinvariantsAbstract: Macdonald polynomials are symmetric functions in a set of variables X which also depend on two parameters q,t. In this talk we describe how a formula of Haiman for the Hilbert series of the quotient ring of diagonal coinvariants in terms of Macdonald polynomials implies a much simpler expression for the Hilbert series involving matrices satisfying certain constraints.

5:00 pm   in 147 Altgeld Hall,  Thursday, March 29, 2012
 Del Edit Copy
Submitted by funk3.
 Vyron Vellis (UIUC Math)3-dimensional constructions in Geometric Function TheoryAbstract: In this talk I will present some 3-dimensional constructions in Geometric Function Theory made by Gehring and V\"ais\"al\"a which are generated by quasicircles and simple domains. We will investigate under which conditions on these simple domains, are these constructions quasispheres or quasiballs. If time permits I will present another construction which is made by Jang-Mei Wu and I. This talk will be accessible to every graduate student.

Tuesday, April 3, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, April 3, 2012
 Del Edit Copy
Submitted by jathreya.
 Joshua Bowman (Stony Brook)Basins of infinity for polynomial maps of $\mathbb{C}^2$Abstract: Basins of attraction in holomorphic dynamics are well understood in dimension 1, much less so in higher dimensions. We will consider regular polynomial maps of $\mathbb{C}^2$ (maps which extend to endomorphisms of $\mathbb{P}^2$) and describe some tools for studying their basins of infinity. We show that there exist endomorphisms of $\mathbb{P}^2$ whose basins of infinity have infinitely generated second homology.

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, April 3, 2012
 Del Edit Copy
Submitted by ford.
 Benjamin Smith (INRIA Saclay and Ecole Polytechnique Paris)Point counting on genus 2 curves with real multplicationAbstract: Point counting -- that is, computing zeta functions of curves over finite fields --- is a fundamental problem in algorithmic number theory and cryptography. In this talk, we present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Using our new algorithm, we can compute the zeta function of an explicit RM genus 2 curve over $\mathbb{F}_q$ in $O(\log^5 q)$ bit operations (vs. $O(\log^8 q)$ for the classical algorithm). This, together with a number of other practical improvements, yields a dramatic speedup for cryptographic-sized Jacobians over prime fields, as well as some record-breaking computations. (Joint work with D. Kohel and P. Gaudry)

Topology Seminar
11:00 am   Tuesday, April 3, 2012
 Del Edit Copy
Submitted by franklan.
 No seminar todayAbstract: We resume next week.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, April 3, 2012
 Del Edit Copy
Submitted by phierony.
 Robert E. Jamison (Clemson/UIUC)A Dependency Calculus for Finitary ClosuresAbstract: A closure system consists of a ground set $X$ together with a family $\mathscr{C}$ of closed subsets of $X$. The only requirements are that $\mathscr{C}$ is closed under arbitrary intersections and contains $X$. Thus each subset $S$ of $X$ lies in a smallest closed set $\mathscr{C}(S)$. The map $S \to \mathscr{C}(S)$ is the closure operator. The closure operator is finitary provided whenever $p \in \mathscr{C}(S)$, there is a finite subset $E$ of $S$ with $p \in \mathscr{C}(E)$. In this talk a first order logic for finitary closure operators will be presented. This first order logic can be used to describe and systematize the study of most important properties of finitary systems. In particular, I will describe a classification scheme for many of the important classes of finitary closures (matroids, antimatroids, partial order convexity, etc). Moreover, I will describe several metatheorems concerning classical convexity invariants such as the Helly and Radon numbers.

Algebra, Geometry and Combinatoric
2:00 pm   in 345 Altgeld Hall,  Tuesday, April 3, 2012
 Del Edit Copy
Submitted by darayon2.
 Bridget Tenner (DePaul University)Repetitions and patternsAbstract: A permutation $w$ can be written as a product of adjacent transpositions, and such a product of shortest length, $\ell(w)$, is called a reduced decomposition of $w$. The difference between $\ell(w)$ and the number of distinct letters appearing in a (any) reduced decomposition of $w$ is $\text{rep}(w)$; that is, this statistic describes the amount of repetition in a reduced decomposition of $w$. In this talk, we will explore this statistic $\text{rep}(w)$, and find that it is always bounded above by the number of 321- and 3412-patterns in $w$. Additionally, these two quantities are equal if and only if $w$ avoids the ten patterns 4321, 34512, 45123, 35412, 43512, 45132, 45213, 53412, 45312, and 45231.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, April 3, 2012
 Del Edit Copy
Submitted by kkirkpat.
 Jun Yin (U Wisconsin-Madison)Eigenvalue and Eigenvector distributions of Random matricesAbstract: In the current study of the random matrix theory, many long time open problems have been solved in the past three years. Right now, the study of the distribution of individual eigenvalues, even eigenvectors has become possible. In some works, we even obtained some brand new formulas which were not predicted before. And our methods have been successfully applied on many different matrix ensembles, like (generalized) Wigner matrix, covariance matrix, band matrix, Erdoes-renyi Graph, correlation matrix, etc. In this talk, besides the recent process on random matrix theory, we will also introduce the main open questions in this field.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 3, 2012
 Del Edit Copy
Submitted by katz.
 Sheldon Katz   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Quantum Cohomology of Toric VarietiesAbstract: The structure of the quantum cohomology ring of a smooth projective toric variety was described by Batyrev and proven by Givental as a consequence of his work on mirror symmetry. This talk is in part expository since some details were never written down by Givental. I conclude with some open questions related to the quantum cohomology ring and the quantum product. An extension of these questions play a foundational role in the development of quantum sheaf cohomology which has been undertaken jointly with Donagi, Guffin, and Sharpe. Given a smooth projective variety X and a vector bundle E with $c_i(E)=c_i(X)$ for i=1,2, the quantum sheaf cohomology ring of string theory is supposed to be a deformation of the algebra $H^*(X,\Lambda^*E^*)$. If E=TX, quantum sheaf cohomology is the same as ordinary quantum cohomology.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 3, 2012
 Del Edit Copy
Submitted by west.
 Thomas Mahoney (UIUC Math)Extending graph choosability results to paintabilityAbstract: Introduced independently by Schauz and by Zhu, the Marker-Remover game is an on-line version of list coloring. The resulting graph parameter, paintability, is at least the list chromatic number (also known as "choosability"). We strengthen several choosability results to paintability. We study paintability of joins with complete or empty graphs. We determine upper and lower bounds on the paintability of complete bipartite graphs. We characterize 3-paint-critical graphs and show that claw-free perfect graphs with $\omega(G)\le3$ have paintability equal to chromatic number. Finally, we introduce and study sum-paintability, the analogue of sum-choosability.

Mathematics in Science and Society (MSS)
4:00 pm   in 245 Altgeld Hall,  Tuesday, April 3, 2012
 Del Edit Copy
Submitted by kapovich.
 Igor Rivin (Temple University)Conformal matching of proteinsAbstract: The question of whether two proteins can bind, and how, is one of the canonical problems in molecular biology, where it is sometimes known as the protein docking problem. This question has, so far, been studied primarily by ad hoc methods (such as Monte Carlo simulation). In this talk I will discuss some ideas and work in progress (some joint with Joel Hass of UC Davis) on using discrete (and not so discrete) conformal geometry to attack the problem, and the interesting (to the speaker, anyhow) mathematical questions which arise.

Wednesday, April 4, 2012

Algebraic Geometry Seminar
3:00 pm   in 145 Altgeld Hall,  Wednesday, April 4, 2012
 Del Edit Copy
Submitted by seminar.
 Alain Couvreur (INRIA Saclay and Ecole Polytechnique Paris)A construction of codes based on the Cartier operatorAbstract: We present a new construction of codes from algebraic curves which is suitable to provide codes on small fields. The approach involves the Cartier operator and can be regarded as a natural generalisation of classical Goppa codes. As for algebraic geometry codes, lower bounds on the parameters of these codes can be obtained by algebraic geometric methods.

Thursday, April 5, 2012

IMSE
10:00 am   in 314 Altgeld Hall,  Thursday, April 5, 2012
 Del Edit Copy
Submitted by seminar.
 Richard Griffith, Ph.D., Senior Manager (Complex Systems for National Security, Sandia National Laboratory)An Overview of Sandia National Laboratories and Our Key Complex Systems National Security ChallengesAbstract: Sandia National Laboratories is a multidisciplinary engineering laboratory dedicated to solving the nation's most difficult national security challenges. Sponsored by the Department of Energy/National Nuclear Security Administration (DOE/NNSA), Sandia has responsibility for the stewardship of the Nation's nuclear weapon stockpile. In addition, the Labs are actively engaged with multiple government agencies to address challenges in nuclear non-proliferation, renewable energy technologies, border and air transit security, conventional military systems, and other important issues. Because many of the key challenges the nation faces are Complex Systems, Sandia has a core capability in complex systems techniques, methods, algorithms, and approaches, and seeks to apply them in unique and creative ways to address these challenges. A number of these complex systems challenges will be discussed, with the intent of identifying faculty and graduate students with aligned research interests.

Number Theory Seminar
11:00 am   in 243 Altgeld Hall,  Thursday, April 5, 2012
 Del Edit Copy
Submitted by ford.
 Jingjing Huang (Penn State Math)Sums of unit fractionsAbstract: The results presented in this talk are joint work of Robert Vaughan with myself. We are mainly concerned with the Diophantine equation $$\frac{a}{n}=\frac1{x_1}+\frac1{x_2}+\cdots+\frac1{x_k}$$ and its number of positive integer solutions $R_k(n;a)$. Now the distribution of the function $R_2(n;a)$ is well understood. More precisely, by averaging over $n$, the first moment and second moment behaviors of $R_2(n;a)$ have been established. Furthermore, we have shown that, after normalisation, $R_2(n;a)$ satisfies Gaussian distribution, which is an analog of the classical theorem of Erdos and Kac. Now, in this talk, I will mainly talk about the following result. Let $E_a(N)$ denote the number of $n\le N$ such that $R_2(n;a)=0$. It is established that when $a\ge3$ we have $$E_a(N)\sim C(a) \frac{N(\log\log N)^{2^{m-1}-1}}{(\log N)^{1-1/2^m}},$$ with $m$ defined in the talk. This result significantly improves a result of Hoffmeister and Stoll. I will explain how to prove this theorem. The next project would be to study the ternary case $k=3$. While the conjecture, by Erd\H{o}s, Straus and Schinzel, that for fixed $a\ge 4$, we have $R_3(n;a)>0$ when $n$ is sufficiently large, is still wide open, here I will talk about some partial results on the mean value $\sum_{n\le N}R_3(n;a)$ if time permits.

Lunch Seminar on NetMath
12:00 pm   in 102 Altgeld Hall (Illinois Geometry Lab),  Thursday, April 5, 2012
 Del Edit Copy
Submitted by gfrancis.
 George Francis   [email] (Mathematics, Urbana)On a Suite of Tools for Online Geometry Courses.Abstract: Absent any single adequate tool for implementing even the most essential online equivalents to standard classroom methods in teaching geometry, my students and I cobbled together a suite of minimally functional tools enabling a now four year old pedagogical experiment. In this presentation I will develop an "axiomatic" wish list of what one needs for an online geometry course. I will illustrate it using the custom tools when possible, and wave my hands when there are none.

Group Theory
1:00 pm   in 347 Altgeld Hall,  Thursday, April 5, 2012
 Del Edit Copy
Submitted by jathreya.
 Jayadev Athreya (UIUC)Radial Density in Apollonian Circle PackingsAbstract: Given an Apollonian Circle Packing (ACP) $P$ and a circle $C_0 = \partial B(z_0, r_0)$ in $P$, color the set of disks in $P$ tangent to $C_0$ red. Take the concentric circle $C_{\epsilon} = \partial B(z_0, r_0 + \epsilon)$. As $\epsilon \rightarrow 0$, what proportion of $C_{\epsilon}$ is red? In joint work with F. Boca, C. Cobeli, and A. Zaharescu, we show that the answer is $3/\pi$.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, April 5, 2012
 Del Edit Copy
Submitted by aimo.
 Pekka Pankka (University of Helsinki, Finland)Almost sure limits of quasiconformally equivalent closed manifoldsAbstract: Suppose $(M_i,p_i)$ is a sequence of pointed closed Riemannian manifolds so that the diameters of $M_i$ grow without bounds. By Gromov's compactness theorem, under conditions on curvature and injectivity radius, this sequence has a subsequence converging in the pointed Gromov-Hausdorff topology to a pointed Riemannian manifold $(X,p)$. But what is $X$ typically like? Under the additional condition that manifolds $M_i$ are uniformly quasiconformally equivalent to a fixed manifold, $X$ is almost surely (in a suitable sense) quasiconformal to either the Euclidean space or a punctured Euclidean space. In this talk I will discuss this and similar results for surfaces and graphs and the relation of these results to the work of Benjamini and Schramm. This is joint work with Hossein Namazi and Juan Souto.

2:00 pm   in 241 Altgeld Hall,  Thursday, April 5, 2012
 Del Edit Copy
Submitted by lukyane2.
 Grace Work (UIUC Math)Ideal Triangulations of Hyperbolic 3-ManifoldsAbstract: In this talk we will see how link complements can be decomposed into finite unions of ideal tetrahedra. From this decomposition we can compute the hyperbolic structure on these manifolds. The tetrahedra provide us with information we can use to compute arithmetic invariants of the manifolds. Our main example will be the complement of the figure-eight knot.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, April 5, 2012
 Del Edit Copy
Submitted by beder.
 Yu Xie (Notre Dame Math)An extension of a Lemma of Huneke to non $m$-primary ideals and formulas for the generalized Hilbert coefficientsAbstract: Let $(R,m)$ be a Cohen-Macaulay local ring and $I$ an $m$-primary ideal. In 1996, Huckaba provided a $d$-dimensional version of a 2-dimensional formula due to Huneke. This formula relates the length $\lambda(I^{n+1}/JI^n)$ to the difference $P(n+1)-H(n+1)$, where $J$ is a minimal reduction of $I$, and $P(n+1)$ and $H(n+1)$ are Hilbert polynomial and Hilbert function of $I$ respectively. We extend the formula further to non $m$-primary ideals and use it to compute the generalized Hilbert coefficients defined by Polini and Xie recently.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, April 5, 2012
 Del Edit Copy
Submitted by kapovich.
 Sijue Wu (University of Michigan)Wellposedness of the two and three dimensional full water wave problemAbstract: We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.

Friday, April 6, 2012

Women's Seminar
11:00 am   in 447 Altgeld Hall,  Friday, April 6, 2012
 Del Edit Copy
Submitted by funk3.
 Jane Butterfield (UIUC Math)Syllabus Construction for Math TA's Abstract: Do you think of your syllabus as a way to give students your contact information and the name of the textbook? As a TA, do you even think you need to hand out a syllabus? This talk will focus on the ways in which a well-written syllabus can help you avoid many common classroom problems. It will be based on the paper "The Purposes of a Syllabus", by J. Parkes and M.B. Harris, interpreted to address the specific needs of graduate students who are TA's for math department courses. We will go to lunch afterwards. If you would like to go to lunch, but can't attend the talk, please meet in the mailroom at 11:50.

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, April 6, 2012
 Del Edit Copy
Submitted by phierony.
 Philipp Hieronymi (UIUC)The Pila-Wilkie theory: The rational points of a definable setAbstract: We will continue our series of talks on the paper 'The rational points of a definable set' by Pila and Wilkie. In this talk, we start looking at the number-theoretic part of the paper (Section 6) and give a full proof of Proposition 6.1, the main ingredient from number theory. Number theorists welcome! The next talk will be on Friday, April 13th.

Monday, April 9, 2012

Special Job Talk
4:00 pm   in 245 Altgeld Hall,  Monday, April 9, 2012
 Del Edit Copy
Submitted by seminar.
 Career Opportunities in Math presents "Epic"Abstract: Pizza and soda to follow with the speaker. Abstract: Trying to decide what to do after graduation? Don’t just get a job. Do something Epic. Epic is one of the world’s premiere healthcare technology firms. We work with many of the largest and most prestigious healthcare organizations in the country and around the world to improve patient care. We have grown steadily over the last 33 years, and currently our software is used to care for about 140 million people across the United States. That means over 40% of Americans will be impacted by the work you do. Epic has an innovative culture that is ideal for new grads who want to work hard and push the limits. We're looking to hire people who want to immediately jump into challenging work and make a difference in the lives of providers and patients across the country. At Epic you’ll collaborate with bright minds from all over the world and take ownership of meaningful projects early on, whether you’re working as a Project Manager, a Problem Solver/Technical Consultant, or a Software Developer. One visit to Epic and you’ll notice that we take our work very seriously – ourselves, not so much. With nine themed office buildings, a tree house conference room, and a gourmet cafeteria, our 800+ acre campus will stimulate your creativity and inspire you to push yourself and your coworkers to continually raise the bar. We offer generous compensation packages, including the benefits you would expect from a leading software company. All of our positions are located in Madison, WI, and relocation expenses are covered by Epic. Epic hires from all majors, all degrees, and all experience levels. If you want to be a part of something bigger, something truly important, consider a career at Epic. You will take on some of the biggest challenges facing the healthcare system. You can check out our available positions and apply at http://www.careers.epic.com. If you are interested in a role at Epic, you can also submit your resume through our website, http://www.epic.com/forms/application.php

Tuesday, April 10, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by ford.
 Andrew Shallue (Illinois Wesleyan Univ. Math)A sieve strategy for irreducible tabulationAbstract: An interesting open problem is to prove that $x^n + x^3 + 1$ is irreducible over $\mathbb{F}_2[x]$ infinitely often. While searching for a better algorithmic method for tabulating such irreducibles, Jonathan Webster and I have developed a sieving strategy which is rare in such settings. The Legendre Sieve provides an initial result on the sparseness of such polynomials with no small factors.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by franklan.
 Qayum Khan (University of Notre Dame)Rigidity of pseudo-free group actions on contractible manifoldsAbstract: Joint with Frank Connolly (U Notre Dame) and Jim Davis (Indiana U). We discuss Quinn's equivariant generalization of the Borel Conjecture. This concerns cocompact proper actions of a discrete group $\Gamma$ on a Hadamard manifold $X$. We give a complete solution when the action of $\Gamma$ is pseudo-free and when $X$ more generally is a $\mathrm{CAT}(0)$ manifold. Here, pseudo-free means that the singular set is discrete. A rich class of examples is obtained from crystallographic groups $\Gamma$ made out of isometric spherical space form groups $G$. If $\Gamma$ has no elements of order two, then we obtain equivariant topological rigidity of the pair $(X, \Gamma)$. Hence, if $\Gamma$ is torsion-free, then we generalize a recent theorem of A. Bartels and W. Lück, which validates the classical Borel Conjecture for $\mathrm{CAT}(0)$ fundamental groups. Otherwise, if $\Gamma$ has elements of order two, we show how to parameterize all possible counter-examples, in terms of Cappell's $\mathrm{UNil}$ summands of the L-theory of infinite dihedral groups. In certain cases, these are detected along hypersurfaces in the orbifold $X / \Gamma$ by generalized Arf invariants.

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by jathreya.
 Maxim Arnold (Department of Mathematics, University of Illinois at Urbana-Champaign)On the identical configurations of abelian sandpile model.Abstract: The Abelian sandpile model was introduced by Bak in the attempt to describe avalanche formations. During the next two decades it was intensively studied and many connections to the similar models was discovered. In particular the set of most often configurations of ASM can be considered as a representation of very natural abelian group. I shall shortly introduce the dynamics corresponding to ASM and state some results concerning identity of this group acting on Sierpinski graph.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by ssolecki.
 Slawomir Solecki (Department of Mathematics, University of Illinois at Urbana-Champaign)Abstract approach to Ramsey theory and Ramsey theorems for finite treesAbstract: I will show how certain Ramsey results for finite trees (some old, some new) are obtained by applying an abstract approach to Ramsey theory. A streamlined version of this abstract approach will be explained in the talk.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by rsong.
 Yufeng Shi (University of Central Florida and Shandong University )Backward Stochastic Integral EquationsAbstract: In this talk we introduce a Volterra type of backward stochastic integral equations, i.e. so called backward stochastic Volterra integral equations (BSVIEs in short), which are natural generalization of backward stochastic differential equations (BSDEs in short). We will present some survey of old and introductory results, followed by some most recent developments, including M-solutions, S-solutions, C-solutions, Lp solutions, multi-dimensional comparison theorem, and mean-field BSVIEs. Main motivations of studying such kind of equations are as follows: (i) in studying optimal controls of (forward) stochastic Volterra integral equations, such kind of equations are needed when a Pontryagin type maximum principle is to be stated; (ii) in measuring dynamic risk for a position process in continuous time, such an equation seems to be suitable; (iii) when a differential utility needs to be considered with possible time-inconsistent preferences, one might want to use such equations.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by kkirkpat.
 Nevena Maric   [email] (U Missouri - St Louis)A construction of bivariate distributions with arbitrary marginals and specified correlationAbstract: We propose a simple and efficient algorithm for exact generation of bivariate samples from two arbitrary (possibly different) marginal distributions and with any attainable correlation coefficient (positive or negative). Our algorithm is related to the ideas of trivariate reduction (introduced by Arnold in 1967) in a sense that we use three independent uniforms in order to obtain a pair of correlated variables with desired marginals. This way we construct a bivariate distribution that is a mixture of Fr\'echet bounds and marginal products. The method allows for fast simulation, and does not have any theoretical limitation in terms of types of distributions and ranges of correlations. [joint work with Vanja Dukić]

Algebra, Geometry and Combinatoric
2:00 pm   in 345 Altgeld Hall,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by darayon2.
 Peter McNamara (Stanford)Finite dimensional representations of KLR algebras Abstract: Khovanov-Lauda-Rouqier algebras are a family of algebras that appear in categorifying quantum groups. I will talk about the category of finite-dimensional representations of these algebras - classifying the simple representations, giving some understanding of higher Ext groups, and the related combinatorial structures. No previous knowledge of KLR algebras will be assumed.

Algebraic Geometry
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by nevins.
 Sarah Kitchen (Albert-Ludwigs-Universität Freiburg)Koszul categories and mixed Hodge modulesAbstract: In this talk, I will report on joint work with Pramod Achar. We considered the following problem: Can we generate a Koszul category from the category of mixed Hodge modules on a smooth complex variety X (constructible along an affine stratification S) by a general procedure, which gives a grading on the category of S-constructible rational perverse sheaves on X? We were motivated by the fact that in their paper on Koszul Duality, Beilinson, Ginzburg and Soergel (BGS) produce their grading from mixed Hodge modules in a way specific to the Bruhat stratification of a flag variety, whereas their approach to l-adic perverse sheaves was more general. I will explain how to "winnow" the category of mixed Hodge modules to come up with the desired Koszul category, and how to obtain a grading on S-constructible perverse sheaves from this, plus the relationship to the grading obtained by BGS.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by west.
 Robert E. Jamison (UIUC and Clemson University)Convexity Partition Numbers and MatchingsAbstract: In 1921 Radon showed that any $d+2$ points in ${\mathbb R}^d$ can be partitioned into two parts so that the convex hulls of the parts have nonempty intersection. In 1966 Tverberg generalized Radon's theorem to partitions into $m$ parts. These notions carry over naturally to any abstract space with a notion of convex hull. For such a space, the $m$-th partition number is the smallest integer $p_m$ such that any $p_m$ points can be partitioned into $m$ parts with the convex hulls of the parts having nonempty intersection. Radon's theorem for $m=2$ and Tverberg's theorem in general yield $p_m = (m-1)(d+1)+1$ for ordinary convexity on ${\mathbb R}^d$. Calder conjectured that Euclidean convexity is the extremal case: $p_m \le (m-1)(p_2-1)+1$ for any abstract convexity space. Eckhoff popularized this, now known as the Partition Conjecture. In 1981 Jamison used matchings in graphs to prove the Partition Conjecture for a class of convexities including partially ordered sets, trees, certain semilattices, and related structures. The purpose of this talk is to solicit improvements of Jamison's matching results that yield additional bounds on partition numbers.

Wednesday, April 11, 2012

Algebraic Geometry
3:00 pm   in 141 Altgeld Hall,  Wednesday, April 11, 2012
 Del Edit Copy
Submitted by schenck.
 Dror Varolin (SUNY-Stonybrook)Hermitian Algebraic GeometryAbstract: Hermitian Algebraic Geometry is the study of certain Hermitian forms on the dual space of polynomials of a given degree, or more generally on duals of spaces of global holomorphic sections of a holomorphic line bundle over a complex manifold.  In this talk I will try survey some part of the subject, mentioning some of the main results and unsolved problems.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, April 11, 2012
 Del Edit Copy
Submitted by seminar.
 Zoi Rapti (Department of Mathematics, University of Illinois at Urbana-Champaign)DNA modeling and Klein-Gordon chainsAbstract: We will start with an overview of how we can model DNA taking into account only the major interactions between the nucleobases. This is coarse-grained enough that will later allow us to use Klein-Gordon equations to describe the DNA dynamics. In particular, we will focus on time-periodic spatially localized solutions and we will use Floquet theory to analyze their linear stability.

Thursday, April 12, 2012

Special Topology Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, April 12, 2012
 Del Edit Copy
Submitted by franklan.
 Daniel Cohen (Louisiana State University)Topological complexity of configuration spacesAbstract: The topological complexity of a space is a homotopy type invariant motivated by the motion planning problem from robotics. We discuss this invariant in the context of configuration spaces of ordered points on orientable surfaces.

Number Theory
11:00 am   in 241 Altgeld Hall,  Thursday, April 12, 2012
 Del Edit Copy
Submitted by berndt.
 Hei-Chi Chan (University of Illinois at Springfield)Some questions related to the Rogers-Ramanujan continued fractionAbstract: The Rogers-Ramanujan continued fraction is defined by $R(q):= \cfrac{ q^{1/5} }{ 1+\cfrac{ q}{ 1+\cfrac{ q^2 }{ 1+\cfrac{ q^3 }{ \ddots } } } } ,$ with $|q|<1$. In this talk, we will look at some results and open questions related to $R(q)$. We will also look at some related concepts, such as the Rogers-Ramanujan identities, $t$-cores, and boson-fermion correspondence. Among other things, we will look at the following integral: $\sqrt{4 \phi + 3 } \,\, - \,\phi = 1 + \exp \left( -\frac{1}{5} \int_{e^{-2\pi}}^1 \frac{ (1-t)^5 (1-t^2)^5 (1-t^3)^5 \cdots \, }{ (1-t^{5}) (1-t^{10}) (1-t^{15}) \cdots \, } \cdot \frac{dt}{t} \right) ,$ where $\phi:=(1 + \sqrt{5})/2$ is the Golden Ratio.

NetMath Lunch Seminar
12:05 pm   in Altgeld Hall,  Thursday, April 12, 2012
 Del Edit Copy
Submitted by gfrancis.
 George Reese and Ken Travers   [email] (Education, UIUC)MSTE Past, Present, and FutureAbstract: In this talk we will give background on the Office for Mathematics, Science, and Technology Education (MSTE). The Office was created in 1993 with a goal to catalog and promote math, science, and technology education programs at the University. Since then, the mission has evolved to one of public engagement that emphasizes partnerships with K-12 schools to integrate technology and improve curriculum. In this talk Reese and Travers will highlight some of the key collaborations MSTE has had and discuss future directions.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, April 12, 2012
 Del Edit Copy
Submitted by kapovich.
 Hao Liang (University of Illinois at Chicago)Centralizers of finite subgroups of the mapping class group and almost fixed points in the curve complexAbstract: Let S be an orientable surface of finite type, MCG(S) the mapping class group of S, C(S) the curve complex of S and H a finite subgroup of MCG(S). By the hyperbolicity of C(S), there exists points in C(S) whose H-orbit has diameter at most 6\delta; We call such points H-almost fixed points. We prove that there exists a constant K depending only on S so that if the diameter of the set of H- almost fixed points is greater than K then the centralizer of H in MCG(S) is infinite. I will start by explaining the proof of the analogous statement for hyperbolic groups, then I will explain the extra ingredients needed for the case of mapping class groups.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, April 12, 2012
 Del Edit Copy
Submitted by aimo.
 Kai Rajala (University of Jyväskylä, Finland)Optimal assumptions for discretenessAbstract: A celebrated theorem of Reshetnyak's says that a non-constant Sobolev mapping F of R^n is discrete and open if K_F=|DF|^n/det(DF) is uniformly bounded. In view of applications to non-linear elasticity theory, geometric function theory, and certain PDE:s, it is desirable to find the minimal analytic assumptions under which one can conclude discreteness and openness. In dimension two, Iwaniec and Sverak proved that it suffices to assume K_F to be locally integrable. We discuss higher-dimensional versions of the Iwaniec-Sverak theorem due to Manfredi and Villamor, and others, and present our joint work with Stanislav Hencl, showing that the expected sharp higher-dimensional version does not hold.

2:00 pm   in 241 Altgeld Hall,  Thursday, April 12, 2012
 Del Edit Copy
Submitted by lukyane2.
 Kelly Funk (Department of Mathematics, University of Illinois at Urbana-Champaign)Rigidity Across DynamicsAbstract: We will discuss the notions of rigidity and uniform rigidity for dynamical systems. We will explore the structure of these sequences and attempt to characterize them.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, April 12, 2012
 Del Edit Copy
Submitted by beder.
 Paulo Mantero (Purdue Math)Liaison classes of non-licci idealsAbstract: A vast part of literature on liaison via complete intersections adresses questions relative to licci ideals, that is, ideals that are in the linkage class of a complete intersection. For a non-licci ideal I, there are few results describing the structure of the linkage class of I, most of them dealing with the case of height 2 ideals (Rao, Lazarsfeld, Ballico-Bolondi-Migliore, Perrin, Martin-Descamps, Nagel, etc.). In particular one would like to find distinguished elements in every linkage class. In this talk we introduce a theoretical definition for minimal' ideals in any even linkage class. We show that, under reasonable assumptions, these ideals exist and are essentially unique. Among all ideals in an even linkage class, these ideals minimize homological invariants (e.g. Betti numbers, multiplicity). We provide several concrete situations where one can identify these minimal elements (e.g. determinantal ideals or ideals with homogeneous linear resolutions are minimal in their respective even linkage classes). If time permits, I will show an application to producing more evidence towards the Buchsbaum-Eisenbud-Horrocks Conjecture.

Spring Department Faculty Meeting
4:00 pm   in 245 Altgeld Hall,  Thursday, April 12, 2012
 Del Edit Copy
Submitted by seminar.
 Spring Department Faculty Meeting

5:00 pm   in 147 Altgeld Hall,  Thursday, April 12, 2012
 Del Edit Copy
Submitted by funk3.
 Anton Lukyanenko (Department of Mathematics, University of Illinois at Urbana-Champaign)Non-Euclidean analysisAbstract: Many tools in analysis are based on the assumption of Euclidean geometry. One uses inner products, covering lemmas and other local properties of R^n. Focusing on the example of Sobolev maps into the Heisenberg group, I will show how analysis is different in the non-Euclidean world.

Friday, April 13, 2012

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, April 13, 2012
 Del Edit Copy
Submitted by phierony.
 Philipp Hieronymi (Department of Mathematics, University of Illinois at Urbana-Champaign)The Pila-Wilkie theory: The rational points of a definable setAbstract: We will continue our series of talks on the paper 'The rational points of a definable set' by Pila and Wilkie. In this talk we present the proof of Theorem 1.10, the main result of the paper. If time permits, the Pila-Zannier proof of the Manin-Mumford Conjecture using the estimates of Pila-Wilkie will be discussed.

Tuesday, April 17, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, April 17, 2012
 Del Edit Copy
Submitted by jathreya.
 Slawomir Solecki (Department of Mathematics, University of Illinois at Urbana-Champaign)Point realizations of Boolean actionsAbstract: We will look at measure preserving Boolean actions of Polish groups and consider the problem, going back to Mackey, of determining when such actions have point realizations. We will explore the boundary line between the groups whose all Boolean actions have point realizability and those that do not have this property. One result, joint with Kwiatkowska, states that Boolean action of Polish groups of isometries of locally compact separable metric spaces can always be point realized. On the other hand, a very recent result with Moore, states that the group of all continuous functions from an uncountable compact space to the circle does not have the point realizability property. In several respects, this last group is quite different from other groups that were shown earlier, by Vershik, Becker and Glasner-Weiss, not to have the point realizability property. Connections with the solution to Hilbert's 5-th problem, with the concentration of measure phenomena, and with the Cameron-Martin theorem will be mentioned.

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, April 17, 2012
 Del Edit Copy
Submitted by ford.
 Atul Dixit (Department of Mathematics, University of Illinois at Urbana-Champaign)Generalized higher order spt-functionsAbstract: We give a new generalization of the spt-function of G.E. Andrews, namely $Spt_j(n)$, and give its combinatorial interpretation in terms of successive lower-Durfee squares. We then generalize the higher order spt-function $spt_k(n)$, due to F.G. Garvan, to ${_j}spt_{k}(n)$, thus providing a two-fold generalization of $spt(n)$, and give its combinatorial interpretation. This is joint work with Ae Ja Yee.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, April 17, 2012
 Del Edit Copy
Submitted by franklan.
 Kevin Costello (Northwestern University)The elliptic genus from quantum field theoryAbstract: Witten proposed that the elliptic genus of a manifold should be the partition function of a certain sigma-model. I'll describe a rigorous version of this result, which also has an interpretation in derived algebraic geometry.

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, April 17, 2012
 Del Edit Copy
Submitted by rdeville.
 Lee DeVille   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Noisy Perturbations of Kuramoto OscillatorsAbstract: We consider the Kuramoto model of coupled oscillators with various couplings and additive white noise. Synchronous solutions which are stable without the addition of noise become metastable and there are transitions amongst synchronous solutions on long timescales. We compute these timescales and, moreover, compute the most likely path in phase space that transitions will follow. We compute these timescales for various families of connection graphs and show that for several families, these timescales do not increase as the system size increases (i.e the action governing the large deviation timescale does not depend significantly on the number of oscillators).

Geometry Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, April 17, 2012
 Del Edit Copy
Submitted by sba.
 Matthew Wright (Huntington University)Hadwiger Integration and ApplicationsAbstract: Integration of integer-valued functionals with respect to Euler characteristic has surprising applications in problems arising in sensor networks, as Rob Ghrist demonstrated in the Trjitzinsky Lectures. This integration theory makes use of Euler characteristic as a topological invariant for counting objects detected by the network. However, Euler characteristic is only one of n+1 Euclidean-invariant valuations on "tame" subsets of n-dimensional Euclidean space. Integration of integer-valued functionals with respect to any of these valuations is straightforward. We can extend this integration theory to real-valued functionals to obtain what we call Hadwiger integrals. The Hadwiger integrals provide various notions of the size of a functional. This talk will explain the theory of Hadwiger integration and discuss some of its challenges and potential applications.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 17, 2012
 Del Edit Copy
Submitted by west.
 Frank R. Bernhart (visitor, Department of Mathematics, University of Illinois at Urbana-Champaign)Enumeration of special classes of outerplanar graphsAbstract: Arrange $n$ vertices equally spaced on a circle, labeled in counterclockwise order. Join some pairs by edges, drawn as chords without crossings. This general class has many interesting subfamilies, some of which can be counted using basic methods of enumeration, especially Lagrange Inversion. Catalan numbers and their generalizations arise frequently. We consider several such families: (1) Polygons with $n$ sides and $r$ diagonals whose bounded regions have $k$ sides. (2) Trees (no crossings allowed!). (3) Graphs where every component is a triangle (requiring components to be edges yields a familiar family counted by the Catalan numbers). (4) Every component is a vertex, an edge, or a cycle (plus subfamilies defined by forbidding isolated vertices or by forbidding edges joining consecutive points). Finally, we also consider supplementing these techniques by Burnside's Lemma when drawings are considered to be equivalent under rotation and reflection, yielding for example an enumeration of maximal outerplanar graphs.

Department Awards Ceremony
4:00 pm   in 314 A&B Illini Union,  Tuesday, April 17, 2012
 Del Edit Copy
Submitted by seminar.
 Department Awards CeremonyAbstract: The Department of Mathematics Awards Ceremony will be held at 4 p.m. in Room 314 A&B Illini Union. Awards will be presented to undergraduate students, graduate students, faculty and staff. Please join us for a reception immediately following the presentation of awards.

Wednesday, April 18, 2012

GEAR Brown Bag
12:00 pm   in Altgeld Hall 331,  Wednesday, April 18, 2012
 Del Edit Copy
 Steve Bradlow (Department of Mathematics, University of Illinois at Urbana-Champaign)Quadratic differentials as Higgs fieldsAbstract: Bring your lunch and join us for informal discussion of all matters relating to GEometric structures And Representation varieties. This week we'll definitely talk about quadratic differentials and Higgs bundles. GEAR will provide cookies. Thanks to the miracle of teleconferencing not all participants will be in the room.

Study Seminar in Geometry and Analysis
3:00 pm   in 345 Altgeld Hall,  Wednesday, April 18, 2012
 Del Edit Copy
Submitted by jathreya.
 Pierre Albin (Department of Mathematics, University of Illinois at Urbana-Champaign)Compactness of Isospectral SurfacesAbstract: We will continue our discussion of the paper of Osgood-Phillips-Sarnak.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, April 18, 2012
 Del Edit Copy
Submitted by seminar.
 Zhong-Jin Ruan (Department of Mathematics, University of Illinois at Urbana-Champaign)Operator Algebras--Noncommutative Topological/Measure Spaces

Thursday, April 19, 2012

Number Theory Seminar
11:00 am   in 243 Altgeld Hall,  Thursday, April 19, 2012
 Del Edit Copy
Submitted by ford.
 Andrew Schultz (Wellesley College, MA)A generalization of the Gaussian Formula and q-analog of Fleck's congruenceAbstract: In the early 1900's, Fleck proved that alternating sums of binomial coefficients taken across particular residue classes modulo a prime number are highly divisible by that prime number. In this talk, I'll discuss some recent work for analogous sums of q-binomial coefficients, and we'll see that these give "half" of a generalization of Fleck's result. This represents a project that I worked on with (then UIUC undergrad) Robert Walker.

NetMath Lunch Seminar
12:05 pm   in 102 Altgeld Hall,  Thursday, April 19, 2012
 Del Edit Copy
Submitted by gfrancis.
 Andrew Schultz   [email] (Wellesley College, MA)NetMath and C&M as a Catalyst for Pedagogical InnovationAbstract: I came to UIUC as a postdoc in 2007 and was assigned a Calculus & Mathematica course because of an image I had on my webpage. Only later did I find out that the perspectives of Uhl, Davis and Porta influenced the way I was taught linear algebra at Davidson College, and that my time as an instructor in the C&M series would in turn shape my own perspective on effective teaching practices. In this talk I'll discuss how teaching a NetMath or C&M course can impact one's perspective on teaching strategies in the "traditional" classroom.

Group Theory
1:00 pm   in 347 Altgeld,  Thursday, April 19, 2012
 Del Edit Copy
Submitted by nmd.
 Pere Menal Ferrer (Universitat Autonoma de Barcelona)Reidemeister torsion for hyperbolic 3-manifoldsAbstract: Reidemeister torsion is an invariant defined for a CW-complex and a linear representation of its fundamental group. It was first defined in the 1930s by Reidemeister, de Rham and Franz to classify lens spaces in dimension 3, and since then it has proven to be a powerful invariant. In this talk, I will first give a brief review of Reidemeister torsion, and how to define it for a hyperbolic 3-manifold. Then I will introduce a certain class of invariants ${ T_n (M) }$ attached to a hyperbolic manifold $M$, which are defined as the Reidemeister torsion of $M$ with respect to the composition of the holonomy representation of $M$ and the $n$-dimensional fundamental representation of $\mathrm{SL}(n, C)$. I will show that the sequence $\{ \log |T_n(M)| / n^2 \}$ converges to $-\mathrm{Vol}(M)/ 4\pi$ (this is an extension of a result by W. Müller which deals with closed manifolds). Finally, I will discuss how the sequence $\{ T_n (M) \}$ determines and is determined by the complex length spectrum of $M$. This is joint work with Joan Porti.

Probability Seminar (special event)
2:00 pm   in 347 Altgeld Hall,  Thursday, April 19, 2012
 Del Edit Copy
Submitted by jathreya.
 David Stork (Distinguished Research Scientist and Research Director, Rambus Labs, Computational Sensing and Imaging Initiative)Lake Wobegon DiceAbstract: We present sets of n non-standard dice-Lake Wobegon Dice-having the following paradoxical property: On every (random) roll of a set, each die is more likely to roll greater than the set average than less than the set average; in a speci c statistical sense, then, each die is "better than the set average." We defi ne the Lake Wobegon Dominance of a die in a set as the probability the die rolls greater than the set average minus the probability the die rolls less than the set average. We further defi ne the Lake Wobegon Dominance of the set to be the dominance of the set's least dominant die and prove that such paradoxical dominance is bounded above by $(n-2)/n$ regardless of the number of sides s on each die and the maximum number of pips p on each side. A set achieving this bound is called Lake Wobegon Optimal. We give a constructive proof that Lake Wobegon Optimal sets exist for all $n \geq 3$ if one is free to choose $s$ and $p$. We also show how to construct minimal optimal sets, that is, that set that requires the smallest range in the number of pips on the faces. We determine the frequency of such Lake Wobegon sets in the $n = 3$ case through exhaustive computer search and nd the unique optimal $n = 3$ set having minimal $s$ and $p$. We investigate symmetry properties of such sets, and present equivalence classes having identical paradoxical dominance. We construct inverse sets, in which on any roll each die is more likely to roll less than the set average than greater than the set average, and thus each die is "worse than the set average." We show the unique extreme "worst" case, the Lake Wobegon Pessimal set. We speculate on the application of such paradoxical Lake Wobegon Dominance for collusion among agents, such as economic agents, each seeking to be "above average" as often as possible. [Joint work with Jorge Moraleda]

2:00 pm   in 241 Altgeld Hall,  Thursday, April 19, 2012
 Del Edit Copy
Submitted by lukyane2.
 Francesco Bei (Sapienza Università di Roma)L^2 de Rham and Hodge theorems on stratified pseudomanifoldsAbstract: Even when studying smooth objects one often runs into singular spaces, but fortunately these often come with some extra structure: a stratification. After recalling what a stratification is and how they come up, I will show that there exist a class of Riemannian metrics whose L^2 de Rham and Hodge cohomology groups are isomorphic to certain topologically defined intersection cohomology groups with a perversity' that depends on the metric.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, April 19, 2012
 Del Edit Copy
Submitted by kapovich.
 Kevin Ford (Department of Mathematics, University of Illinois at Urbana-Champaign)Prime chains and applicationsAbstract: A sequence of primes $p_1,...,p_k$ is a "prime chain" if $p_j|(p_{j+1}-1)$ for each $j$. For example: 3, 7, 29, 59, 709. We describe new estimates for counts of prime chains satisfying various properties, e.g. the number of chains with $p_k < x$ ($k$ variable) and the number of chains with $p_1=p$ and $p_k \le x$. We discuss some applications of these estimates, in particular the settling of a 50-year old conjecture of Erdos that $\phi(a)=\sigma(b)$ has infinitely many solutions ($\phi$ is Euler's function, $\sigma$ is the sum of divisors function). We also focus on the distribution of $H(p)$, the length of the longest chain ending at a given prime $p$. $H(p)$ is also the height of the "Pratt tree" for $p$, the tree structure of all chains ending at $p$. We give new, nontrivial bounds for $H(p)$, valid for almost all $p$, and settle a conjecture of Erdos, Granville, Pomerance and Spiro from 1990. We introduce and analyze a random model of the Pratt tree, based on branching random walks, which leads to some surprising conjectures about the distribution of $H(p)$. Finally, we give an application to groups with "perfect order subsets" and discuss various open problems in the area.

CAS/MillerComm 2012
5:30 pm   in Room 62, Krannert Art Museum, 500 E. Peabody Drive, Champaign,  Thursday, April 19, 2012
 Del Edit Copy
Submitted by seminar.
 David Stork (Distinguished Research Scientist and Research Director, Rambus Labs, Computational Sensing and Imaging Initiative)When Computers Look at Art: Image Analysis in Humanistic Studies of the Visual ArtsAbstract: What can computers reveal about images that even the best-trained connoisseurs, art historians and artists cannot? How do these computer methods work? How much more powerful and revealing will these methods become? In short, how is computer image analysis changing our understanding of art? This profusely illustrated lecture for non-scientists will include works by Jackson Pollock, Vincent van Gogh, Jan van Eyck and others. You may never see paintings in the same way again. This CAS/MillerComm 2012 Lecture is hosted in part by the Department of Mathematics and the Krannert Art Museum.

Friday, April 20, 2012

Logic Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, April 20, 2012
 Del Edit Copy
Submitted by ssolecki.
 Dana Bartosova (University of Toronto)Universal minimal flows in the language of filtersAbstract: I will introduce a construction by Balcar and Franek of the Boolean algebra of clopen sets of the universal minimal dynamical system for discrete groups. I will show how that generalizes to topological groups. I will talk about a couple of applications of this approach, e.g. to groups of automorphisms of uncountable structures using methods of Kechris, Pestov and Todorcevic connecting structural Ramsey theory and topological dynamics.

Sunday, April 22, 2012

NetMath Lunch Seminar
1:00 pm   in 102 A,  Sunday, April 22, 2012
 Del Edit Copy
Submitted by gfrancis.
 Peter Glaze (Mathematics)To Be Announced

Tuesday, April 24, 2012

Joint Ergodic Theory/Number Theory Seminar
11:00 am   in 347 Altgeld Hall,  Tuesday, April 24, 2012
 Del Edit Copy
Submitted by jathreya.
 Francesco Cellarosi (IAS/MSRI)Ergodic Properties of Square-Free NumbersAbstract: We study binary and multiple correlations for the set of square-free numbers and we construct a dynamical systems naturally associated to them. We prove that such dynamical system has pure point spectrum and it is therefore isomorphic to a translation on a compact abelian group. In particular, the system is ergodic but not weakly mixing, and it has zero metric entropy. The latter results were announced recently by Peter Sarnak and our approach provides an alternative approach. Joint work with Yakov Sinai.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, April 24, 2012
 Del Edit Copy
Submitted by franklan.
 Anna Marie Bohmann (Northwestern University)Global equivariant K-theoryAbstract: Equivariant K-theory is one of the original examples of an equivariant homology theory, but it is surprisingly difficult to construct as an orthogonal spectrum, and thus as a global spectrum. I will highlight some of the difficulties that arise in building good equivariant K-theory spectra and discuss Joachim's construction of equivariant K-theory via $C^*$-algebras. Finally, I will explain why this construction yields a global version of K-theory.

Differential Geometry Seminar
1:00 pm   in 243 Altgeld Hall,  Tuesday, April 24, 2012
 Del Edit Copy
Submitted by sba.
 Steven Rayan (U Toronto Math)Combinatorics of the moduli space of L-twisted Higgs bundles at genus 0Abstract: An L-twisted Higgs bundle on a compact Riemann surface is a vector bundle together E with an L-valued Higgs field, that is, an endomorphism taking values along a fixed line bundle L.  (Ordinary Higgs bundles arise by choosing the canonical line bundle for L.)  The Betti numbers of the moduli space of L-twisted Higgs bundles on P^1, with fixed numerical invariants, can be determined by Hitchin's localization calculation: the Poincar\'e series of the moduli space is the (weighted) sum of Poincar\'e series of certain subvarieties of the nilpotent cone.  These subvarieties are precisely moduli spaces of holomorphic chains: these are chains of vector bundles where the maps are L-twisted Higgs fields.  Some of the difficulty in classifying these chains is avoided in the case of P^1, over which the situation becomes very combinatorial.  I will calculate Betti numbers for certain low values of the rank of E and degree of L, in order to verify some conjectural numbers coming from Mozgovoy's twisted version of Chuang, Diaconescu, and Pan's ADHM formula.  I will also make some conjectures about properties of the Betti numbers, including in the case of arbitrary genus.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, April 24, 2012
 Del Edit Copy
Submitted by laugesen.
 Oscar Lopez-Pamies   [email] (UIUC Civil and Environmental Engineering)Cavitation instabilities in nonlinear elastic solids: a defect-growth formulation based on iterated homogenizationAbstract: I will introduce a new formulation to study cavitation instabilities in nonlinear elasticity. The basic idea is to first cast cavitation as a homogenization problem of nonlinear elastic solids containing random distributions of zero-volume cavities, or defects. This problem is then addressed by means of a novel iterated homogenization procedure. Ultimately, the relevant calculations amount to solving Hamilton-Jacobi equations, in which the initial size of the defects plays the role of time'' and the applied load plays the role of space''. When specialized to the case of isotropic loading conditions, isotropic solids, and vacuous defects, the proposed formulation recovers the classical result of John Ball (1982) for radially symmetric cavitation. I will discuss the nature and implications of this remarkable connection.

Logic Seminar
1:00 pm   in Altgeld Hall,  Tuesday, April 24, 2012
 Del Edit Copy
Submitted by ssolecki.
 Anush Tserunyan (UCLA)Finite generators for countable group actionsAbstract: Consider a Borel action of a countable group $G$ on a standard Borel space $X$. A countable Borel partition $P$ of $X$ is called a generator if $GP=\{ gA: g \in G, A \in P\}$ generates the Borel $\sigma$-algebra of $X$. Existence of such $P$ of cardinality $n$ is equivalent to the existence of a $G$-embedding of $X$ into the shift $n^G$. For $G=Z$, the Kolmogorov-Sinai theorem implies that finite generators don't exist in the presence of an invariant probability measure with infinite entropy. It was asked by Weiss in the late 80s, whether the nonexistence of any invariant probability measure would guarantee the existence of a finite generator. We show that the answer is positive in case $X$ admits a $\sigma$-compact topological realization (e.g. if $X$ is a $\sigma$-compact Polish $G$-space). We also show that finite generators always exist in the context of Baire category thus answering a question of Kechris. In fact, we show that if $X$ is a Polish $G$-space having infinite orbits, then there is a 4-generator on an invariant comeager set.

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, April 24, 2012
 Del Edit Copy
Submitted by kkirkpat.
 Jose Blanchet (Columbia Engineering)A Large Deviations Theory for Heavy-tailed Processes via Martingale Arguments and its Connections to Monte CarloAbstract: Modern large deviations theory centers around the work of Donsker and Varadhan in the setting of processes whose marginal distributions have a finite moment generating. The existence of a finite moment generating function turns out to be crucial for the development of the theory in that it allows to define suitable positive martingales which, in turn, generate changes of measure. In important areas of application such as risk theory and operations research, however, stochastic processes with heavy-tails arise naturally; so no moment generating function exists. Moreover, it is well known (as we shall discuss) that the qualitative features of most likely paths given rare events are completely different in light and heavy tailed settings. One of the most advantageous features of the Donsker-Varadhan theory is that it suggests, via changes of measure, efficient Monte Carlo simulation methods for sampling rare events. In this talk, we present an approach for the large deviations analysis of heavy-tailed processes that is based on changes of measure and thus it is parallel to the Donsker-Varadhan approach in that the analysis suggests efficient Monte Carlo simulation methods for rare events as well. (This talk builds on joint work with P. Glynn and J. C. Liu).

Group Theory (note unusual day)
2:00 pm   in 241 Altgeld Hall,  Tuesday, April 24, 2012
 Del Edit Copy
Submitted by jathreya.
 Shubojoy Gupta (Yale)Asymptoticity of grafting and Teichmuller raysAbstract: We shall discuss a result showing that any grafting ray in Teichmuller space is (strongly) asymptotic to a Teichmuller geodesic ray. Our method involves constructing quasiconformal maps between the underlying Thurston metric of a complex projective surface on one hand, and the singular flat metric induced by a holomorphic quadratic differential on the other. As a consequence we can show that the set of points in Teichmuller space obtained by integer graftings on any hyperbolic surface projects to a dense set in moduli space.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 24, 2012
 Del Edit Copy
Submitted by west.
 Mohsen Jamaali (Sharif University (Iran))On harmonious coloring of graphsAbstract: Let $G$ be a simple graph, and let $\Delta(G)$ denote the maximum degree of $G$. A harmonious coloring of $G$ is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number $h(G)$ is the least number of colors in such a coloring. In this talk, with a constraint on $\Delta(G)$, we determine the exact value of $h(G)$ when $G$ is a tree. Furthermore, some bounds on $h(G)$ are obtained in general for trees and for bipartite graphs. An analogous concept of harmonious edge coloring is introduced, and some results on the harmonious edge-chromatic number are proved.

Wednesday, April 25, 2012

GEAR Brown Bag
12:00 pm   in 331 Altgeld Hall,  Wednesday, April 25, 2012
 Del Edit Copy
 Jayadev Athreya (UIUC Math)Quadratic differentials and billiardsAbstract: Bring your lunch and join us for informal discussion of all matters relating to GEometric structures And Representation varieties. Continuing the discussion on the many facets of quadratic differentials, this week their role in dynamics will be highlighted. GEAR will provide cookies. Thanks to the miracle of teleconferencing not all participants will be in the room.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, April 25, 2012
 Del Edit Copy
Submitted by seminar.
 Aimo Hinkkanen (Department of Mathematics, University of Illinois at Urbana-Champaign)Complex analysis of one variable

Thursday, April 26, 2012

Number Theory Seminar
11:00 am   in 243Altgeld Hall,  Thursday, April 26, 2012
 Del Edit Copy
Submitted by ford.
 Youness Lamzouri (Department of Mathematics, University of Illinois at Urbana-Champaign)Discrepancy bounds for the distribution of the Riemann zeta functionAbstract: In 1930 Bohr and Jessen proved that for any $1/2<\sigma\leq 1$, $\log \zeta(\sigma+it)$ has a continuous limiting distribution in the complex plane. As a consequence they deduced that the set of values of $\log \zeta(\sigma+it)$ is everywhere dense in $\mathbb{C}$. Harman and Matsumoto obtained a quantitative version of the Bohr-Jessen Theorem using Fourier analysis on a multidimensional torus. In this talk we shall present a different approach which leads to uniform discrepancy bounds for the distribution of $\log \zeta(\sigma+it)$ that improve the Matsumoto-Harman estimates.

NetMath Lunch Seminar
12:05 pm   in 102 Altget Hall,  Thursday, April 26, 2012
 Del Edit Copy
Submitted by gfrancis.
 Peter Glaze (Department of Mathematics, University of Illinois at Urbana-Champaign)Peer-led Learning and the Student Experience in NetMathAbstract: One of the most innovative aspects of the NetMath approach to online education is our integral student mentoring system. Qualified undergraduate students assist NetMath instructors, and develop a personal, tutorial relationship with their students. We will discuss how this mentoring system is intimately tied to the learning experience of our students, the pedagogical principles it implements, and our plans for its renovation, improved recruitment and supervision in the future.

Harmonic Analysis and Differential Equations
1:00 pm   in 345 Altgeld Hall,  Thursday, April 26, 2012
 Del Edit Copy
Submitted by bronski.
 Florian Dorfler (UCSB Engineering)Synchronization in Power Networks and Coupled OscillatorsAbstract: We discuss the synchronization and transient stability problem in power networks. We exploit the relationship between the power network model considered in transient stability analysis and the well-known Kuramoto model of coupled phase oscillators. A tight connection between these two models can be rigorously established by means of topological conjugacy arguments. In particular, we show the equivalence of local synchronization conditions in both models. Furthermore, we present novel algebraic conditions for synchronization of coupled Kuramoto oscillators. Our synchronization conditions are necessary and sufficient for particular interconnection topologies and network parameters, they are sufficient in the general case, and they improve upon previously-available tests for the Kuramoto model. In the end, we are able to state concise and purely algebraic conditions that relate synchronization in a power network to certain graph-theoretical properties of the underlying electric network. The results reveal elegant connections between the transient stability problem in power networks and the theory of coupled oscillators and multi-agent dynamical systems.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, April 26, 2012
 Del Edit Copy
Submitted by kapovich.
 Pekka Pankka (University of Helsinki)From Picard's theorem to quasiregular ellipticityAbstract: In the quasiconformal geometry of Riemannian manifolds the classical Picard theorem from complex analysis turns into an existence question for non-constant quasiregular mappings from Euclidean spaces into Riemannian manifolds. In this talk, I will discuss the role of the fundamental group in these questions and a class of metrics, introduced by Semmes, that connect these quesiregular ellipticity questions to questions on quasiconformal geometry of decomposition spaces. This talk is based on joint works with Kai Rajala and Jang-Mei Wu.

2:00 pm   in 241 Altgeld Hall,  Thursday, April 26, 2012
 Del Edit Copy
Submitted by lukyane2.
 Caglar Uyanik (Department of Mathematics, University of Illinois at Urbana-Champaign)What is an Outer Space?Abstract: I will try to explain the construction and the topology of Outer space introduced by Culler and Vogtmann. In particular, I will sketch the proof of contractibility.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, April 26, 2012
 Del Edit Copy
Submitted by kapovich.
 Catharina Stroppel (University of Bonn)Categorification with applications in low-dimensional topologyAbstract: I would like to explain the idea of categorification along the questions: what do we mean by this and why is it useful? The applications presented will be from low dimensional topology and knot theory. The solution and categories involved are however coming from Lie theory and algebraic geometry. The talk should give an overview about the concepts illustrated by a few concrete examples.

5:00 pm   in 147 Altgeld Hall,  Thursday, April 26, 2012
 Del Edit Copy
Submitted by funk3.
 Rami Luisto (University of Helsinki)On the non-existence of BLD-mappings between manifoldsAbstract: I will give my talk about the main result of my Master's thesis [1]. The result can be seen to be a metric version of the Varopoulos theorem, which states that if N is a compact n-dimensional Riemannian manifold whose fundamental group has hyperbolic growth rate, then there exists no quasiregular mapping from the Euclidean n-space to N. In my thesis I translate this result to the metric setting by talking about path-metric manifolds and Bounded Length Distortion (BLD) mappings between them. A BLD mapping, in short, is an open, discrete and continuous mapping that preserves the lengths of rectifiable paths up to a fixed multiplicative constant. In my talk I will introduce the concepts of the growth rate of a finitely generated group, path-length structure of a manifold and the basic properties of Bounded Length Distortion mappings. If we have time left, I will talk about some results of my Licentiate's thesis which embetter the results given in my Master's thesis. There might be chocolate available during the presentation. [1] Luisto, Rami. On the non-existence of BLD-mappings between manifolds.'' Master's thesis, available at http://helsinki.fi/~luisto/ProGradu.pdf

Friday, April 27, 2012

Logic Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, April 27, 2012
 Del Edit Copy
Submitted by phierony.
 Eva Leenknegt (Purdue)In search of p-adic minimality: An exploration of weak p-adic structuresAbstract: Consider a structure (F,L), where F is a field and L is a language that is 'related' to the language of rings, in the sense that the Lring-definable subsets of F coincide with the L-definable subsets of F (that is, we require (F,L) to be 'Lring-minimal'). When F is a real closed field, a structure satisfying this property will be o-minimal, so all tools of o-minimality, such as the cell decomposition theorem, are at our disposal when studying such structures. The situation is less clear when F is a p-adic(ally closed) field. If L is an expansion of the ring languages, then (F,L) will be P-minimal, but very little is known in general for weaker structures (reducts of the ring language) When will a reduct L of the ring language give rise to an Lring-minimal structure? In the o-minimal case, the answer is easy: the only requirement is that the order should be definable in L. Our first challenge will be to find a p-adic equivalent of this 'minimal language' (<). Once such a language has been found, one can start constructing examples of weak p-adic Lring- minimal structures. While a general theory is still far away, individual examples show that there are some fundamental differences when comparing p-adic and o-minimal reducts of the ring language. I will give some examples of this. One of the questions that comes up is the existence of cell decomposition: could it possibly be true that every p-adic Lring-minimal language has cell decomposition? I will discuss some (partial) answers to this question, and show how we can use this to study examples of weak structures.

Algebra, Geometry and Combinatoric
4:00 pm   in 341 Altgeld Hall,  Friday, April 27, 2012
 Del Edit Copy
Submitted by darayon2.
 Allen Knutson (Cornell)Manifold atlases consisting of Bruhat cellsAbstract: A Bruhat cell is a finite-dimensional affine space, but comes with many additional structures: a stratification, a torus action, a Poisson structure, a Frobenius splitting, a totally nonnegative part... When we have a manifold with these structures, we can ask whether it can be given an atlas of charts consisting of Bruhat cells. I'll give a construction of a Coxeter diagram D (sometimes) associated to a manifold M with a stratification Y. If the Bruhat atlas program can be carried out for M, it gives a poset antiisomorphism between Y and an order ideal in the Bruhat order W_D. We have checked this combinatorics ex post facto for partial flag manifolds and wonderful compactifications of groups. The full program is complete for the Grassmannian, where the diagram is the affine Dynkin diagram, by work of [K-Lam-Speyer] and [Snider]. For most other examples, D is neither finite nor affine. This work is joint with Xuhua He and Jiang-Hua Lu.

Tuesday, May 1, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, May 1, 2012
 Del Edit Copy
Submitted by ford.
 Alina Cojocaru (Univ. Illinois Chicago)Frobenius fields for elliptic curvesAbstract: Let E be an elliptic curve defined over $\mathbb{Q}$. For a prime p of good reduction for E, let $\pi_p$ be the $p$-Weil root of E and $\mathbb{Q}(\pi_p)$ the associated imaginary quadratic field generated by $\pi_p$. In 1976, Serge Lang and Hale Trotter formulated a conjectural asymptotic formula for the number of primes $p < x$ for which $\mathbb{Q}(\pi_p)$ is isomorphic to a fixed imaginary quadratic field. I will discuss progress on this conjecture, in particular an average result confirming the predicted asymptotic formula. This is joint work with Henryk Iwaniec and Nathan Jones.

Topology Seminar
11:00 am   Tuesday, May 1, 2012
 Del Edit Copy
Submitted by franklan.
 No seminar todayAbstract: We will resume in the fall.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, May 1, 2012
 Del Edit Copy
Submitted by bronski.
 Mary Pugh   [email]Thin Liquid Films with DrivingAbstract: We present two thin liquid film problems with driving. The first problem is experimentally motivated and considers questions such as steady states and the existence of dynamic solutions. The second problem is more PDE-motivated and considers questions such as the presence (or absence) of finite-time blow-up. In the first problem, we consider a horizontal cylinder, rotating about its center. A viscous fluid is on the outside of the cylinder, coating the cylinder as it rotates. We consider a lubrication approximation of the Navier Stokes equations for the regime in which the fluid film is relatively thin and the surface tension is relatively large. The resulting lubrication model may have no steady state, a unique steady state, or more than one steady state. Using both numerics and analysis, we consider the dynamics of this flow, including whether or not solutions can become singular in finite time. In the second problem, we consider a long-wave unstable thin film problem $u_t = - (u^n u_{xxx})_x - B (u^m u_x)_x. The dynamics are strongly affected by the balance between the exponents n and m. We discuss the subcritical, critical, and supercritical regimes for the equation and present new results for finite-time blow-up for the problem on the line. This is joint work with Marina Chugunova (University of Toronto) and Roman Taranets (Nottingham). Logic Seminar 1:00 pm in 345 Altgeld Hall, Tuesday, May 1, 2012  Del Edit Copy Submitted by ssolecki.  Laurentiu Leustean (Institute of Mathematics of the Romanian Academy)Proof mining in nonlinear analysisAbstract: The program of proof mining is concerned with the extraction of hidden finitary and combinatorial content from proofs that make use of highly infinitary principles. This new information can be both of quantitative nature, such as algorithms and effective bounds, as well as of qualitative nature, such as uniformities in the bounds or weakening the premises. Thus, even if one is not particularly interested in the numerical details of the bounds themselves, in many cases such explicit bounds immediately show the independence of the quantity in question from certain input data. This line of research, developed by Ulrich Kohlenbach in the 90's, has its roots in Georg Kreisel's program on unwinding of proofs, put forward in the 50's. In this talk I will present applications of proof mining to the asymptotic behavior of nonexpansive iterations and nonlinear generalizations of ergodic averages. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, May 1, 2012  Del Edit Copy Submitted by west.  Christian Altomare (The Ohio State University)Antimatroid minors: The Graph Minor Theorem, Laver's Theorem, and Forbidden Antimatroid Minor TheoremsAbstract: This talk is designed to be accessible and (hopefully) of interest to graph theorists and logicians. The Graph Minor Theorem says that every minor closed property of finite graphs has a finite forbidden minor description. (One version of) Laver's Theorem states the same is true for suborder closed properties of countable total orders. A notion of minor for antimatroids, thought of as "combinatorial proof systems", specializes to graph minor and total order embeddability for those respective objects. This allows a conjectural unification of these two seemingly quite distinct theorems. We discuss this unification and antimatroid minor theorems as well. Wednesday, May 2, 2012 GEAR Brown Bag 12:00 pm in 331 Altgeld Hall, Wednesday, May 2, 2012  Del Edit Copy Submitted by bradlow.  Nathan Dunfield (UIUC Math)3-manifolds which fiber over a circle Abstract: Bring your lunch and join us for informal discussion of all matters relating to GEometric structures And Representation varieties, especially (this week) 3-manifolds which fiber over a circle. GEAR will provide cookies. Thanks to the miracle of teleconferencing not all participants will be in the room. Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, May 2, 2012  Del Edit Copy Submitted by seminar.  Vadim Zharnitsky (Department of Mathematics, University of Illinois at Urbana-Champaign)Hamiltonian dynamics and billiard systems Thursday, May 3, 2012 Special Graduate Geometry and Topology Seminar 12:00 pm in 241 Altgeld Hall, Thursday, May 3, 2012  Del Edit Copy Submitted by lukyane2.  Amir Nayyeri (UIUC Computer Science)How to Walk Your Dog in the MountainsAbstract: We describe a O(log n)-approximation algorithm for computing the homotopic Frechet distance between two polygonal curves that lie on the boundary of a surface. Prior to this work, algorithms where known only for curves on the Euclidean plane with polygonal obstacles. A key technical ingredient in our analysis is a$O(\log n)$-approximation algorithm for computing the minimum height of a homotopy between two curves. No algorithms were previously known for approximating this parameter. Surprisingly, it is not even known if computing either the homotopic Frechet distance, or the minimum height of a homotopy, is in NP. Joint work with Sariel Har-Peled, Mohammad Salavatipour and Anastasios Sidiropoulos NetMath Lunch Seminar 12:05 pm in 102 Altgeld Hall, Thursday, May 3, 2012  Del Edit Copy Submitted by gfrancis.  Deanna Raineri [email] (Associate Dean, College of Liberal Arts and Sciences)LAS-Online: A Comprehensive Program for Promoting Online Education in the College of Liberal Arts and Sciences.Abstract: Two years ago, LAS launched LAS OnLine, an initiative to offer many of its high enrolling and high demand courses in a fully online format. Why do we believe that online education is an important part of LAS' mission and, two years in, what have we learned? Illinois Geometry Lab 1:30 pm in 239 Altgeld Hall, Thursday, May 3, 2012  Del Edit Copy Submitted by jathreya.  Illinois Geometry Lab Participants (UIUC)IGL Open HouseAbstract: Please join us for the first Illinois Geometry Lab (IGL) end-of-semester open house. We will be in AH 239 (the Calculus and Mathematica Lab) showcasing undergraduate research in geometry under the direction of UIUC math faculty, staff, and graduate students. Projects range from the mathematical theory of music, to visualizing Minkowski and DeSitter space, to the history of the Altgeld Mathematical Models. Come and meet the students involved and interact with their projects. Geometry Seminar 3:00 pm in 347 Altgeld Hall, Thursday, May 3, 2012  Del Edit Copy Submitted by sba.  Joseph Rosenblatt (UIUC)Partitions for Optimal ApproximationsAbstract: The Riemann integral can be approximated using partitions and a rule for assigning weighted sums of the function at points determined by the partition. Approxi- mation methods commonly used include endpoint rules, the midpoint rule, the trapezoid rule, Simpson’s rule, and other quadrature methods. The rate of approximation depends mostly on the rule being used and the smoothness of the function, but fine structure in this rate of approximation depends on choosing an optimal partition. We discuss how one chooses an optimal partition of points, what is the resulting rate of approximation as the number of points tends to infinity, and how to determine the characteristic distribution of the points in these optimal partitions. Retirement reception 4:00 pm in 321 Altgeld Hall, Thursday, May 3, 2012  Del Edit Copy Submitted by seminar.  Abstract: Please join us at a reception in honor of the retirement of A.J. Hildebrand. Cookies and coffee will be served from 4-5 p.m. in the Common Room. Thursday, June 14, 2012 NetMath Lunch Seminar 12:05 pm in 102 Altgeld Hall (Illinois Geometry Lab), Thursday, June 14, 2012  Del Edit Copy Submitted by gfrancis.  George Francis [email] (UIUC)Common Core Standards in GeometryAbstract: The Common Core State Standards (CCSS) will be implemented by 2015 in schools of the 45 signatory states, including Illinois. Like all such national school initiatives these will have some effect on the way we teach mathematics to future teachers of America. This seminar has a first looks at the CCSS High School Geometry section, since they are most proximate to the netGeometry program in NetMath. Future seminars could include similar looks at other sections, such as statistics, calculus, finite math, logic etc. Pizza will be served. Let me know if you're coming and what flavor pizza you prefer. Please bring your own drinks. Thursday, June 21, 2012 NetMath Lunch Seminar 12:05 pm in 102 Altgeld Hall (Illinois Geometry Lab), Thursday, June 21, 2012  Del Edit Copy Submitted by gfrancis.  Kathleen Rapp Smith (UIUC)Modeling Under the CCSSAbstract: The Common Core State Standards (CCSS) promote modeling of observed phenomena as an appropriate mathematical activity even in the earliest grades. Come and spend a little time with the CCSS in mathematics. We will do examples of modeling as defined under the standards and discuss how working within the standards may change our future students and our preparation of future teachers. Please bring a graphing calculator if possible and a pencil and paper. Pizza will be served, bring your own drink. Tuesday, July 3, 2012 CSL/Math Seminar 11:30 am in 141 CSL, Tuesday, July 3, 2012  Del Edit Copy Submitted by ymb.  Prof. Don Shimamoto (Swarthmore Math)Topology of Configuration Spaces of Polygons in the PlaneAbstract: Consider closed chains, or "polygons," in the plane in which the vertices are free to move about as long as the lengths of the sides remain constant. These objects have been studied in many disciplines, including computer science, engineering, and mathematics, especially over the last twenty years. The set of all configurations of the polygon is a topological space, and this talk is a survey of some of the basic topological techniques and results. Within the space, there are polygons having special properties, and the talk closes with a discussion of the topological type of the spaces of convex and non-self-intersecting configurations. Thursday, July 19, 2012 1:00 pm in Altgeld Hall, Thursday, July 19, 2012  Del Edit Copy Submitted by west.  To Be Announced Monday, July 23, 2012 GEAR Junior Retreat 9:00 am in 314 Altgeld Hall, Monday, July 23, 2012  Del Edit Copy Submitted by jathreya.  GEometric structures And Representation varietiesAbstract: The first Junior Retreat for the GEAR Network will be held July 23 -- August 3, 2012 at the University of Illinois in Urbana-Champaign. The Retreat 2012 will immediately follow the Junior Retreat. The purpose of these retreats is to build bridges between the different interest groups in the network -- and more broadly among mathematicians working in areas relating to GEometric structures And Representation varieties. The Junior Retreat is designed for graduate students and postdocs and has the primary objective of preparing participants to take full advantage of the Retreat 2012. As such, the Junior retreat will focus on providing an introduction to the following five areas: Higgs Bundles; Geometric Structures and Teichmüller Spaces; Dynamics on Moduli Spaces; Special Representations; and Hyperbolic 3-manifolds The Junior Retreat will feature one or two mini-courses on each of these themes; the mini-courses will be supplemented by problem sessions and time for discussion. In addition, there will be shorter research talks given by participants. Read more at http://gear.math.illinois.edu/programs/JuniorRetreat2012.html Monday, August 6, 2012 GEAR Retreat 8:00 am in Altgeld Hall, Monday, August 6, 2012  Del Edit Copy Submitted by jathreya.  GEometric structures And Representation varietiesAbstract: The first Retreat for the GEAR Network will be held August 6 -10, 2012. This will be preceded by the Junior Retreat. The Retreat is designed is to build bridges between the different interest groups in the network - and more broadly among mathematicians working in areas relating to GEometric structures And Representation varieties. Each of the five days of the Retreat will feature one of the following themes: 1.Higgs Bundles 2. Geometric Structures and Teichmüller Spaces 3. Dynamics on Moduli Spaces 4. Special Representations 5. Hyperbolic 3-manifolds There will be two 50 minute lectures in the morning, with the goal of surveying the state-of-the-art, followed by 3 or 4 shorter research lectures in the afternoon. Recognizing that participants will not be equally well versed in all thematic areas, the program will include "everything you ever wanted to know about (X)" sessions led by each day's experts, as well as open discussions designed to identify emerging issues that might benefit from a multidisciplinary approach. Read more at http://gear.math.illinois.edu/programs/SeniorRetreat2012.html Wednesday, August 8, 2012 Mathematical Biology 1:00 pm in Altgeld Hall, Wednesday, August 8, 2012  Del Edit Copy Submitted by rdeville.  To Be Announced Friday, August 10, 2012 Algebra, Geometry and Combinatoric 2:00 pm in 143 Altgeld Hall, Friday, August 10, 2012  Del Edit Copy Submitted by ayong.  Alexander Woo (Univ. of Idaho)Local complete intersection Schubert varietiesAbstract: I will talk about a characterization of the Schubert varieties which are local complete intersections (lci) using pattern avoidance. One direction of the proof is by constructing an explicit minimal set of equations cutting out neighborhoods of Schubert varieties at the identity. This leads to some interesting combinatorics involving Fulton's essential set and the Schubert varieties defined by inclusions, which have a mysterious link to certain hyperplane arrangements called inversion arrangements. The other direction requires a generalization of pattern avoidance known as mesh pattern avoidance. This is joint work with Henning Ulfarsson (Reykjavik U.). Tuesday, August 28, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Tuesday, August 28, 2012  Del Edit Copy Submitted by ford.  Zhi-Wei Sun (Nanjing University)Various new observations about primesAbstract: This talk focuses on the speaker's recent discoveries about primes. We will talk about the speaker's new way to generate all primes or primes in certain arithmetic progressions, and his various conjectures for products of primes, sums of primes, recurrence for primes, representations of integers as alternating sums of consecutive primes. We will also mention his new observations (made in this August at UIUC) about twin primes, squarefree numbers, and primitive roots modulo primes. Probability Seminar 2:00 pm in Altgeld Hall 347, Tuesday, August 28, 2012  Del Edit Copy Submitted by kkirkpat.  David Anderson (UW-Madison)Computational methods for stochastically modeled biochemical reaction networksAbstract: I will focus this talk on computational methods for stochastically modeled biochemical reaction networks. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transitions of the chain. I will show how different computational methods can be understood and analyzed by using different representations for the processes. Topics discussed will be a subset of: approximation techniques, variance reduction methods, parameter sensitivities. Algebraic Geometry Seminar 3:00 pm in 243 Altgeld Hall, Tuesday, August 28, 2012  Del Edit Copy Submitted by choi29.  Julius Ross (University of Cambridge)Maps in Kahler Geometry associated to Okounkov BodiesAbstract: The Okounkov body is a convex body in Euclidean space that can be associated to a projective manifold with a given flag of submanifolds. This convex body generalises certain aspects of the familiar Delzant polytope for toric varieties, although the Okounkov body will not be polyhedral or rational in general. In this talk I will discuss some joint work with David Witt-Nystrom that involves the study of maps from a manifold to its Okounkov body coming from Kahler geometry that are similar to the moment map in toric geometry. I will start by introducing the Okounkov body and the kind of maps that one might like to have, and then give an inductive construction that works in a neighbourhood of the flag. This is acheived through a homogeneous Monge-Ampere equation associated to the degeneration to the normal cone of a divisor, that can be thought of as a kind of "tubular neighbourhood" theorem in complex geometry. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, August 28, 2012  Del Edit Copy Submitted by lidicky.  Zoltán Füredi [email] (UIUC and Renyi Institute, Budapest, Hungary)Optimal Multivalued ShatteringAbstract: We have found an extension of the celebrated Sauer, Perles and Shelah, Vapnik and Chervonenkis result concerning Vapnik-Chervonenkis dimension of 0-1 sequences to$k$-ary codes. This is a joint work with A. Sali. Wednesday, August 29, 2012 Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, August 29, 2012  Del Edit Copy Submitted by laugesen.  Richard Laugesen [email] (UIUC Math)Eigenvalues of the LaplacianAbstract: The fundamental processes of classical physics are diffusion and wave motion. Quantum mechanics too is a kind of wave phenomenon. Mathematically, these processes can all be decomposed in terms of eigenfunctions (states) and eigenvalues (frequencies) of the Laplacian (the sum of pure second partial derivatives). What do we know about those eigenvalues? What would we like to know? I will concentrate on isoperimetric problems that stretch back to Queen Dido in antiquity and Lord Rayleigh in the 19th century, and continue into the future. Thursday, August 30, 2012 Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, August 30, 2012  Del Edit Copy Submitted by katz.  Organizational MeetingAbstract: At this organizational meeting, we will come up with topics of interest to both mathematicians and physicists. We will also be inviting visiting speakers from other campuses once we have identified our common interests. You are welcome to bring a sack lunch if you would like. Please come and bring your suggestions! Group Theory Seminar 1:00 pm in Altgeld Hall 347, Thursday, August 30, 2012  Del Edit Copy Submitted by kapovich.  Organizational meeting Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, August 30, 2012  Del Edit Copy Submitted by collier3.  Informational and Organizational meetingAbstract: It's time for the graduate geometry and topology seminar to start again. We will meet for a short organizational meeting. Everyone in strongly encouraged to attend, especially new first years. COOKIES will be provided. Tuesday, September 4, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, September 4, 2012  Del Edit Copy Submitted by franklan.  Jim McClure (Purdue University)Verdier duality and Poincare dualityAbstract: There is a well-known argument that deduces Poincare duality from Verdier duality. In the lecture I will review the relevant sheaf-theoretic background and show that the isomorphism obtained in this way is the same as the classical isomorphism obtained from the cap product. As a byproduct I will observe that Verdier duality is not actually needed for the well-known argument mentioned above. Everything I will say has an analogue for intersection homology (in particular, Verdier duality is not needed for the proof of Poincare duality in that situation either); I'll say something about this at the end if time allows. Logic Seminar 1:00 pm in 345 Altgeld Hall, Tuesday, September 4, 2012  Del Edit Copy Submitted by phierony.  Andrew Arana (UIUC Philosophy & Math)Transfer in algebraic geometryAbstract: The focal question of this talk is to investigate the value of transfer between algebra and geometry, of the sort exemplified by the Nullstellensatz. Algebraic geometers frequently talk of such transfer principles as a "dictionary" between algebra and geometry, & claim that these dictionaries are fundamental to their practice. We'll first need to get clear on what such transfer consists in. We'll then investigate what how such transfer might improve how knowledge is gathered in algebraic geometric practice. Probability Seminar 2:00 pm in Altgeld Hall 347, Tuesday, September 4, 2012  Del Edit Copy Submitted by kkirkpat.  Michael Damron (Princeton U)Invasion percolation, the incipient infinite cluster and random walks in 2DAbstract: In this talk I will define two percolation models: the invasion percolation cluster (IPC) and the incipient infinite cluster (IIC). Both of these are closely related to critical independent percolation, and have similar critical exponents and fractal structure. I will explain recent results with Phil Sosoe and Jack Hanson (Ph. D. students at Princeton) about quenched subdiffusivity of random walks on both graphs. This extends work of H. Kesten, who showed in the 80's that a random walk on the IIC is subdiffusive in an averaged sense. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, September 4, 2012  Del Edit Copy Submitted by lidicky.  Derrick Stolee [email] (UIUC)Uniquely$K_r$-Saturated Cayley GraphsAbstract: A graph is uniquely$H$-saturated if it contains no copy of$H$but adding any missing edge creates exactly one copy of$H$. In the case of$H$being a complete graph, very little is known about which graphs are uniquely$K_r$-saturated. The only two infinite families previously known are books and the complements of odd cycles. In this talk, we will discuss two new infinite families of uniquely$K_r$-saturated graphs which are complements of Cayley graphs with small generator sets. One of these proofs is the first example of using discharging to bound the clique number of a graph. This is joint work with Stephen G. Hartke. Wednesday, September 5, 2012 Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, September 5, 2012  Del Edit Copy Submitted by laugesen.  Philipp Hieronymi [email] (UIUC Math)An invitation to Mathematical LogicAbstract: I will give a short introduction to Mathematical Logic and the research carried out by members of the Logic group here in Urbana. I will present some of the fundamental theorems of Mathematical Logic established in first part of the 20th century, and then compare these to the research done today. Thursday, September 6, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, September 6, 2012  Del Edit Copy Submitted by ford.  Bruce Berndt (UIUC Math)Unpublished Manuscripts Published with Ramanujan's Lost NotebookAbstract: Published with Ramanujan's lost notebook are several partial manuscripts. Some evidently were intended to be portions of papers that he had published. Others are partial manuscripts of papers that were never completed. In this lecture, we discuss examples of both types. For the former, we offer speculation on why Ramanujan never included the results in his published papers. The manuscripts are over a broad range of topics, including classical analysis, analytic number theory, diophantine approximation, and elementary mathematics. Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, September 6, 2012  Del Edit Copy Submitted by katz.  Olabode Sule (Illinois Physics)von Neumann and Renyi Entanglment entropy in 2D CFTsAbstract: For a given partition of the Hilbert space in quantum mechanical systems, we can ask how degrees of freedom in one part are entangled with those in the other. The entanglement entropy (the von Neumann and Renyi entanglement entropy) is a useful measure to quantify such entanglement. It has been proven to be a useful tool to study various properties of quantum field theories. We will review some results on the entanglement entropy in two-dimensional conformal field theories, focusing on how much information we can get from the scaling of the entanglement entropy. We would describe how the entanglement Renyi entropy is related to the construction of Riemann surfaces by gluing. Graduate Geometry Topology Seminar 2:00 pm in 241, Thursday, September 6, 2012  Del Edit Copy Submitted by collier3.  Anton Lukyanenko (UIUC Math)What is geometric group theory and who cares?Abstract: How do you tell if two groups are isomorphic? This is an extremely difficult task, but in certain cases attaching geometric notions to the groups makes it tractable and leads to new, intriguing geometries. The main example will come from the Heisenberg group, which with a (sub-)Riemannian metric becomes one of the 8 Thurston geometries. Commutative Ring Theory 3:00 pm in 243 Altgeld Hall, Thursday, September 6, 2012  Del Edit Copy Submitted by s-dutta.  Organizational Meeting Mathematics Colloquium 4:00 pm in 245 Altgeld Hall 245, Thursday, September 6, 2012  Del Edit Copy Submitted by kapovich.  Sheldon Katz (Departments of Mathematics and Physics, University of Illinois at Urbana-Champaign)A Mathematician’s Search for The Higgs BosonAbstract: The Higgs boson is the only elementary particle occurring in the Standard Model of physics which has not yet been conclusively observed experimentally, although a new particle sharing some characteristics of the sought-for Higgs has been recently observed at the Large Hadron Collider in Geneva and reported on extensively in the media. In this talk, I will explain the Higgs boson and the Standard Model in the language of modern mathematics. In particular, I will explain how the Higgs boson causes other elementary particles to acquire mass, and relate the theory to recent experiments at the LHC. Friday, September 7, 2012 Analysis Seminar 2:00 pm in 241 Altgeld Hall, Friday, September 7, 2012  Del Edit Copy Submitted by aimo.  Gaven Martin (Massey University, New Zealand)The solution to Siegel's ProblemAbstract: We outline the history and the proof of the identification of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3 Coxeter group extended by the involution preserving the symmetry of this diagram. This solves (in three dimensions) the problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the signature formula identifying the (2,3,7)-triangle group as having minimal co-area. There are strong connections with arithmetic hyperbolic geometry in the proof and the result has applications in the maximal symmetry groups of hyperbolic 3-manifolds (in much the same way that Hurwitz 84g-84 theorem and Siegel's result do). Saturday, September 8, 2012 Department Fall Picnic 1:00 pm in Hessel Park, Champaign, Saturday, September 8, 2012  Del Edit Copy Submitted by seminar.  Department Fall PicnicAbstract: The Department of Mathematics fall picnic will be held from 1 to 4 p.m. at Hessel Park in Champaign. Please bring a dish to share. Beverages, table service, and grilled meats will be provided. Monday, September 10, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall , Monday, September 10, 2012  Del Edit Copy Submitted by mbrannan.  Sepideh Rezvani (UIUC Math)Hilbert C*-modulesAbstract: Sepideh will introduce the notion of a Hilbert C*-module. Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, September 10, 2012  Del Edit Copy Submitted by fcellaro.  Francesco Cellarosi [email] (UIUC)Statistical Mechanics of k-free Numbers and Smooth Sums Estimates. Abstract: I will present a generalization of a previous work by Ya.G. Sinai and myself concerning certain sparse sets of k-free integers, equipped with a complex measure. After rescaling, it turns out that the distribution of these integers is approximated by self-convolutions of the Dickman-De Bruijn distribution. Using the language of Statistical Mechanics, this result gives a thermodynamical limit for our ensembles. As an application, we get asymptotic estimates of certain smooth sums over smooth k-free integers. Tuesday, September 11, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, September 11, 2012  Del Edit Copy Submitted by franklan.  Ben Ward (Purdue University)From pre-Lie to BVAbstract: We will investigate several extensions of the notion of an operad and consider algebraic structures encoded by and arising from them, including (pre-)Lie, Frobenius, Gerstenhaber and BV structures. Then, motivated by topological questions, we will study the example of$A_{\infty}$Frobenius algebras and the associated BV (resp. homotopy BV) structure on the Hochschild cohomology (resp. cochains). This is partially joint work with Ralph Kaufmann and Javier Zuniga. Logic Seminar 1:00 pm in 345 Altgeld Hall, Tuesday, September 11, 2012  Del Edit Copy Submitted by phierony.  Andrew Arana (UIUC Philosophy and Math)Transfer in algebraic geometry - Part IIAbstract: The focal question of this talk is to investigate the value of transfer between algebra and geometry, of the sort exemplified by the Nullstellensatz. Algebraic geometers frequently talk of such transfer principles as a "dictionary" between algebra and geometry, & claim that these dictionaries are fundamental to their practice. We'll first need to get clear on what such transfer consists in. We'll then investigate what how such transfer might improve how knowledge is gathered in algebraic geometric practice. --- This talk is a continuation of the talk given in the Logic seminar last week. Enough of a survey of what has come before will be given so that people who missed the first talk, can still attend this talk with profit. Harmonic Analysis and Differential Equations 1:00 pm in 347 Altgeld Hal, Tuesday, September 11, 2012  Del Edit Copy Submitted by vzh.  Jeremy Louis Marzoula [email] (UNC Math)Quasilinear Schroedinger EquationsAbstract: In this talk, we will discuss joint works with Jason Metcalfe and Daniel Tataru on short time local well-posedness in low-regularity Sobolev spaces for quasilinear Schrödinger equations. Such results are refinements of the pioneering works by Kenig-Ponce-Vega and Kenig-Ponce-Rolvung-Vega, where viscosity methods were used to prove existence of solutions in very high regularity spaces. Our arguments however are purely dispersive. The function spaces in which we show existence are constructed in ways motivated by the results of Mizohata, Ichinose, Doi, and others, including the same authors related to local smoothing estimates. Geometry Seminar 2:00 pm in 243 Altgeld Hall, Tuesday, September 11, 2012  Del Edit Copy Submitted by sba.  Pierre Albin (UIUC Math)Compactness of relatively isospectral sets of surfacesAbstract: Although one can not hear the shape of a drum', it turns out that the set of isospectral metrics on a closed surface forms a compact set. I will discuss joint work with Clara Aldana and Frédéric Rochon regarding the corresponding statement for non-compact surfaces. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, September 11, 2012  Del Edit Copy Submitted by lidicky.  Bernard Lidicky [email] (UIUC Math)Peeling the GridAbstract: Consider the set of points formed by the$n\times n$grid, and the process that in each iteration removes from the point set the vertices of its convex-hull. Here, we prove that the number of iterations of this process is$O(n^{4/3})$; that is, the number of convex layers of the$n\times n$grid is$\Theta(n^{4/3})$. This is joint work with Sariel Har-Peled. Wednesday, September 12, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Wednesday, September 12, 2012  Del Edit Copy Submitted by mbrannan.  Sepideh Rezvani (UIUC Math)Hilbert C*-modules, Part IIAbstract: We will continue our discussion of Hilbert C*-modules. Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, September 12, 2012  Del Edit Copy Submitted by laugesen.  John D'Angelo [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Inequalities from Complex AnalysisAbstract: After a short discussion about complex analysis in one and several variables, I discuss two specific interesting inequalities about integrals. In each case I give two proofs (in the one variable setting) to help glimpse deeper waters. Thursday, September 13, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, September 13, 2012  Del Edit Copy Submitted by ford.  Dermot McCarthy (Texas A&M)Hypergeometric Functions over Finite Fields and Modular FormsAbstract: Hypergeometric functions over finite fields were introduced by Greene in the 1980's as analogues of the classical hypergeometric function. His motivation was to bring some order' to the area of character sums and their evaluations by appealing to the rich theory of the classical function, and, in particular, its transformation properties. Since then, these finite field hypergeometric functions have also exhibited interesting properties in other areas. In particular, special values of these functions have been related to the Fourier coefficients of certain elliptic modular forms. Relationships with Siegel modular forms of higher degree are also expected. We will outline recent work on proving an example of such a connection, whereby a special value of the hypergeometric function is related to an eigenvalue associated to a Siegel eigenform of degree 2. This is joint work with Matt Papanikolas. Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, September 13, 2012  Del Edit Copy Submitted by katz.  Rob Leigh (Illinois Physics)Berezin Integration: the Physics Analysis Seminar 2:00 pm in 243 Altgeld Hall, Thursday, September 13, 2012  Del Edit Copy Submitted by aimo.  Vasileios Chousionis (UIUC Math)Singular integrals, self-similar sets and removability in the Heisenberg group. (Joint work with P. Mattila)Abstract: We study singular integrals on lower dimensional subsets of metric groups where the main examples we have in mind are Euclidean spaces and Heisenberg groups. We prove a general unboundedness criterion for singular integrals which extends results in Euclidean spaces to more general kernels than previously considered. Moreover it can be used in order to determine the critical dimension for removable sets of Lipschitz harmonic functions in the Heisenberg group, in an analogous way as in the Euclidean case. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, September 13, 2012  Del Edit Copy Submitted by collier3.  Peter Nelson (UIUC Math)What is a (co)homology theory and why you should care.Abstract: The main goal of algebraic topology is to study spaces via various algebraic invariants. I'll give a brief introduction to the primary type of these invariants, namely, homology and cohomology theories. Examples and "geometric" applications will abound. Commutative Ring Theory 3:00 pm in 243 Altgeld Hall, Thursday, September 13, 2012  Del Edit Copy Submitted by s-dutta.  Javid Validashti (UIUC Math)On Syzygies and Singularities of Tensor Product SurfacesAbstract: On Syzygies and Singularities of Tensor Product Surfaces. Let$U \subseteq H^0({\mathcal{O}_{\mathbb{P}^1 \times \mathbb{P}^1}}(2,1))$be a basepoint free four-dimensional vector space. We study the associated bigraded ideal$I_U \subseteq \textsf{k}[s,t;u,v]$from the standpoint of commutative algebra, proving that there are exactly six numerical types of possible bigraded minimal free resolution. These resolutions play a key role in determining the implicit equation for the image of the projective surface in$\mathbb{P}^3$parametrized by generators of$U$over$\mathbb{P}^1 \times \mathbb{P}^1$. This problem arises from a real world application in geometric modeling, where one would like to understand the implicit equation and singular locus of a parametric surface. This talk is based on a joint work with H. Schenck and A. Seceleanu. Mathematics Colloquium 4:00 pm in 245 Altgeld Hall, Thursday, September 13, 2012  Del Edit Copy Submitted by kapovich.  David Borthwick (Emory University)Resonances of hyperbolic surfacesAbstract: The spectral theory of compact hyperbolic surfaces is an old topic with many interesting results, many of which originate in Atle Selberg's approach to the study of automorphic forms. Selberg's techniques also extend to non-compact surfaces of finite area, although the analysis is somewhat more difficult in this case. For hyperbolic surfaces of infinite area, however, much of the method that was so successful in the compact setting appears to fail. Although the basic spectral properties of such manifolds were worked out in the 1980's by Lax and Phillips, there were no clear infinite-area analogs for the beautiful results of the Selberg theory at that point. This situation started to change in the mid-1990's. Breakthroughs in geometric scattering theory, and in the theory of resonances in particular, have given us in the last 15 years a much more complete picture of the spectral theory of hyperbolic surfaces of infinite area. Many results of the Selberg theory from the compact case do turn out to have very close analogs in this setting, even though the spectral theory is radically different. In this talk we will attempt to give an accessible introduction the spectral theory of hyperbolic surfaces. After highlighting some of the classical results of the Selberg theory, our main goal will be to explain recent developments in the infinite-area case. Friday, September 14, 2012 Model Theory and Descriptive Set Theory Seminar 3:00 pm in 345 Altgeld Hall, Friday, September 14, 2012  Del Edit Copy Submitted by phierony.  Slawomir Solecki (UIUC Math)Unitary representations of oligomorphic groupsAbstract: We will discuss the paper "Unitary representations of oligomorphic groups" by T. Tsankov (GAFA, (2) 22 (2012), 528-555). This will be the first talk of a series about this paper. Monday, September 17, 2012 Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, September 17, 2012  Del Edit Copy Submitted by fcellaro.  Andrew Parrish (UIUC)Convergence of Sparse Subset Averages of$L^1$Functions.Abstract: The behavior of time averages when taken along subsets of the integers is a central question in subsequence ergodic theory. The existence of transference principles enables us to talk about the convergence of averaging operators in a universal sense; we say that a sequence$\{a_n\}$is universally pointwise good for$L^1$, for example, if the sequence of averages \begin{equation*} \frac{1}{N} \sum_{n=0}^{N-1} f \circ \tau^{-a_n}(x) \end{equation*} converges a.e. for any$f\in L^1$for every aperiodic measure preserving system$(X, \mathcal{B}, \mu, \tau)$. Only a few methods of constructing a sparse sequence that is universally pointwise$L^1$-good are known. We will discuss how one can construct families of sets in$\mathbb{Z}^d$which are analogues of these sequences, as well as some challenges and advantages presented by these higher-dimensional averages. Joint work with P. LaVictoire (University of Wisconsin, Madison) and J. Rosenblatt (UIUC). Operator Algebra Learning Seminar 10:00 pm in 147 Altgeld Hall, Monday, September 17, 2012  Del Edit Copy Submitted by mbrannan.  Sepideh Rezvani (UIUC MAth)Hilbert C*-modules, Part III Tuesday, September 18, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, September 18, 2012  Del Edit Copy Submitted by franklan.  Sean Tilson (Wayne State University)Power operations and the Kunneth Spectral SequenceAbstract: Power operations have been constructed and successfully utilized in the Adams and Homological Homotopy Fixed Point Spectral Sequences by Bruner and Bruner-Rognes. It was thought that such results were not specific to the spectral sequence, but rather that they arose because highly structured ring spectra are involved. In this talk, we show that while the Kunneth Spectral Sequence enjoys some nice multiplicative properties, the obvious algebraic operations are zero (other than the square). Despite the negative results we are able to use old computations of Steinberger's with our current work to compute operations in the homotopy of some relative smash products. Logic Seminar 1:00 pm in 345 Altgeld Hall, Tuesday, September 18, 2012  Del Edit Copy Submitted by phierony.  Mia Minnes (UC San Diego)Algorithmic Randomness via Random AlgorithmsAbstract: Algorithmic randomness defines what it means for a single mathematical object to be random. This active area of computability theory has been particularly fruitful in the past several decades, both in terms of expanding theory and increasing interaction with other areas of math and computer science. Randomness can be equivalently understood in terms of measure theory, descriptive complexity, and martingales. In this context, we present a novel definition of betting strategies that uses probabilistic algorithms also studied in complexity theory. This definition leads to new characterizations of several central notions in algorithmic randomness and addresses Schnorr's critique, a longstanding philosophical question in algorithmic randomness. Moreover, these techniques suggest new approaches for tackling one of the biggest open questions in the field (KL = ML?). This is joint work with Sam Buss. Probability Seminar 2:00 pm in Altgeld Hall 347, Tuesday, September 18, 2012  Del Edit Copy Submitted by kkirkpat.  Todd Kemp (UCSD Math)Liberation of Random ProjectionsAbstract: Given two subspaces of a finite dimensional space, there is a minimal dimension their intersection can have; when this dimension is minimized the subspaces are said to be in general position. Easy 19th Century mathematics shows that any two subspaces are almost surely'' in general position in many senses. One modern precise meaning we can give to this statement is as follows: perform a Brownian motion on the unitary group (of rotations), applied to one of the subspaces. Then for any fixed positive time, the Brownian rotated subspaces are almost surely in general position, regardless of starting configuration. What happens if the ambient space is an infinite dimensional Hilbert? While there is no unitarily invariant measure, it is still possible to make sense of the unitary Brownian motion and its action on some (but not all) subspaces. However, the easy techniques for proving the general position theorem are unavailable. Instead, one can apply stochastic analysis and free probability techniques to to analyze a spectral measure associated to the problem. In this talk, I will discuss probabilistic and PDE techniques that come into play in proving the general position theorem in infinite dimensions. This is joint work with Benoit Collins. Algebra, Geometry and Combinatorics 2:00 pm in 345 Altgeld Hall, Tuesday, September 18, 2012  Del Edit Copy Submitted by bwyser.  Ben Wyser [email] (UIUC Math)Geometry and Combinatorics of K-Orbits on the Flag ManifoldAbstract: The orbits of a symmetric subgroup on a flag manifold ("K-orbits") are of importance in the representation theory of real Lie groups, and have been studied extensively from this perspective. The closures of such orbits are generalizations of Schubert varieties, and any geometric and/or combinatorial question one has about Schubert varieties can equally well be posed about these more general orbit closures. However, while the geometry and combinatorics of Schubert varieties have been studied exhaustively, even apart from their role in representation theory, K-orbits and their closures have received far less attention from these perspectives. I will discuss the K-orbit analogue of a story which is well understood in the case of Schubert varieties. Namely, I will describe how one can compute representatives for the torus-equivariant cohomology classes of K-orbit closures, and how these formulas can be interpreted as Chern class formulas for certain types of degeneracy loci. This is in parallel with the well-known story, due to Lascoux-Schutzenberger, Fulton, Pragacz, Graham, et. al., of double Schubert polynomials as representatives for the torus-equivariant classes of Schubert varieties, and their interpretation as Chern class formulas for the classes of degeneracy loci associated to flagged vector bundles. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, September 18, 2012  Del Edit Copy Submitted by lidicky.  Matthew Yancey [email] (UIUC Math)Color-Critical Graphs With Few EdgesAbstract: A graph$G$is$k$-critical if it has chromatic number$k$, but every proper subgraph of$G$is$(k-1)$-colorable. Let$f_k(n)$denote the minimum number of edges in an$n$-vertex$k$-critical graph. We give a bound on$f_k(n)$that is exact for every$n=1\,({\rm mod }\, k-1)$. It is also exact for$k=4$and every$n\geq 6$. The result improves the classical bounds by Gallai and Dirac and subsequent bounds by Krivelevich and Kostochka and Stiebitz. It establishes the asymptotics of$f_k(n)$for every fixed$k$. We also present some applications of the result, in particular, a simple proof of the Grotzsch Theorem that every triangle-free planar graph is$3$-colorable. This is joint work with Alexandr Kostochka. Academic Job Search Panel 4:00 pm in 243 Altgeld Hall, Tuesday, September 18, 2012  Del Edit Copy Submitted by kmortens.  Math Dept. faculty membersAcademic Job Search PanelAbstract: This meeting will focus on the basics of the academic job search in mathematics - postdocs, jobs at colleges, universities, etc. There will be lots of time for questions. Current and former grad directors from our department as well as some people who have been through a job search recently will be there to answer all your questions. Feel free to attend even if you are not finishing this year – it can be helpful to look ahead early! Wednesday, September 19, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Wednesday, September 19, 2012  Del Edit Copy Submitted by mbrannan.  Sepideh RezvaniHilbert C*-modules, Part IV Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, September 19, 2012  Del Edit Copy Submitted by laugesen.  Alexandr Kostochka [email] (UIUC Math)On k-color-critical n-vertex graphs with fewest edgesAbstract: A graph$G$is$k$-{\em critical} if it has chromatic number$k$, but every proper subgraph of$G$is$(k-1)$--colorable. Let$f_k(n)$denote the minimum number of edges in an$n$-vertex$k$-critical graph. We give a lower bound,$f_k(n) \geq F(k,n)$, that is sharp for every$n=1\,({\rm mod }\,$It is also sharp for$k=4$and every$n\geq 6$. The result improves the classical bounds by Gallai and Dirac and some subsequent bounds. It establishes the asymptotics of$f_k(n)$for every fixed$k$. It also proves that the conjecture by Ore from 1967 that for every$k\geq 4$and$n\geq k+2$,$f_k(n+k-1)=f(n)+\frac{k-1}{2}(k - \frac{2}{k-1})$holds for each$k\geq 4$for all but at most$k^3/12$values of$n$. The result has interesting applications. One of the corollaries of the theorem is a half-page proof of the theorem due to Gr\" otzsch that every triangle-free planar graph is$3$-colorable. Thursday, September 20, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, September 20, 2012  Del Edit Copy Submitted by ford.  Harold Diamond (UIUC Math)Chebyshev bounds for Beurling generalized numbersAbstract: This is a semi-expository talk. It begins with a survey of Beurling generalized numbers, a structure that is similar to rational integers, except for having only multiplicative structure. We seek conditions on the counting function of g-numbers that allow us to deduce analogs of the Chebyshev upper and lower prime bounds. An early conjecture of the speaker is shown to be inadequate, and further conditions are given for which the bounds hold. The results are proved to be optimal in their class. Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, September 20, 2012  Del Edit Copy Submitted by katz.  Sheldon Katz (Illinois Math)Supermanifolds and Berezin IntegrationAbstract: This is an expository talk on the mathematical formalism of supermanifolds, which provides a rigorous way to analyze the "anticommuting coordinates" of physics used in the study of fermions. I will also introduce Berezin integration, a mathematical formalism which gives a precise meaning to fermionic integration as it arises in physics. I would like to say something as well about supersymmetry but I won't promise due to time constraints. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, September 20, 2012  Del Edit Copy Submitted by collier3.  Mike DiPasquale (UIUC Math)Bezout, Cayley-Bacharach, and PascalAbstract: We introduce some basic constructions of algebraic geometry in the process of exploring the geometry of curves in the complex projective plane. In particular we will discuss Bezout's theorem and the Cayley-Bacharach theorem for plane cubics, pointing out the special case of Pascal's 'mystic hexagon.' The object is to communicate the power of algebraic machinery in proving some beautiful geometric theorems. Women's Seminar 3:00 pm in 147 Altgeld Hall, Thursday, September 20, 2012  Del Edit Copy Submitted by funk3.  Sarah Loeb and Sogol Jahanbekam (UIUC Math)Combinatorics at MightyAbstract: Results in Chromatic-Paintability and the Paintability of Complete Bipartite Graphs by Sarah Loeb Introduced independently by Schauz and by Zhu, the Marker-Remover game is an on-line version of list coloring. The game is played on a graph$G$with a token assignment$f$giving each$v \in V(G)$a nonnegative number of tokens. On each round Marker marks a subset$M$of the remaining vertices, which uses up a token on each vertex in$M$. Remover deletes from the graph an independent subset of vertices in$M$. Marker wins by marking a vertex that has no tokens. Remover wins if the entire graph is removed. The paint number, or paintability, of a graph$G$is the least$k$such that Remover has a winning strategy when$f(v) = k$for all$v \in V(G)$. We show that if$G$is$k$-paintable and$|V(G)| \le \frac{t}{t-1} k$, then the join of$G$with$\overline{K}_t$is$(k+1)$-paintable. As a corollary, the paint number of$G$equals to its chromatic number when$|V(G)| \le \chi(G) + 2 \sqrt{\chi(G)-1}$. This strengthens a result of Ohba. We also explore the paintability of complete bipartite graphs. Extending a result of Erd\H{o}s, Rubin, and Taylor,$K_{k,r}$is$k$-paintable if and only if$r < k^k$. For$j \ge 1$we provide an upper bound on the least$r$such that$K_{k+j,r}$is not$k$-paintable. 1,2,3-Conjecture and 1,2-Conjecture for sparse graphs by Sogol Jahanbekam We apply the Discharging Method to prove the 1, 2, 3-Conjecture and the 1, 2-Conjecture for graphs with maximum average degree less than 8 3. As a result, the conjectures hold for planar graphs with girth at least 8. Commutative Ring Theory 3:00 pm in 243 Altgeld Hall, Thursday, September 20, 2012  Del Edit Copy Submitted by s-dutta.  Javid Validashti (UIUC Math)On Syzygies and Singularities of Tensor Product SurfacesAbstract: On Syzygies and Singularities of Tensor Product Surfaces. Let$U \subseteq H^0({\mathcal{O}_{\mathbb{P}^1 \times \mathbb{P}^1}}(2,1))$be a basepoint free four-dimensional vector space. We study the associated bigraded ideal$I_U \subseteq \textsf{k}[s,t;u,v]$from the standpoint of commutative algebra, proving that there are exactly six numerical types of possible bigraded minimal free resolution. These resolutions play a key role in determining the implicit equation for the image of the projective surface in$\mathbb{P}^3$parametrized by generators of$U$over$\mathbb{P}^1 \times \mathbb{P}^1$. This problem arises from a real world application in geometric modeling, where one would like to understand the implicit equation and singular locus of a parametric surface. This talk is based on a joint work with H. Schenck and A. Seceleanu. Fall Department Faculty Meeting 4:00 pm in 245 Altgeld Hall, Thursday, September 20, 2012  Del Edit Copy Submitted by seminar.  Fall Department Faculty Meeting Friday, September 21, 2012 Model Theory and Descriptive Set Theory Seminar 3:00 pm in 347 Altgeld Hall, Friday, September 21, 2012  Del Edit Copy Submitted by phierony.  Slawomir Solecki (UIUC Math)Unitary representations of oligomorphic groups - CANCELLED Abstract: This talk is cancelled. We will continue our series of talks about the paper "Unitary representations of oligomorphic groups" by T. Tsankov (GAFA, (2) 22 (2012), 528-555) on Friday September 28th. Monday, September 24, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Monday, September 24, 2012  Del Edit Copy Submitted by mbrannan.  Marius Junge (University of Illinois, Department of Mathematics)Hilbert W*-Modules, Part II Abstract: Marius will continue the discussion on Hilbert W*-modules from last Wednesday. Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, September 24, 2012  Del Edit Copy Submitted by jathreya.  Joe Rosenblatt (University of Illinois, Department of Mathematics)Directional Behavior for Two-variable Commuting ActionsAbstract: Directional ergodicity and directional weak mixing of the action of two commuting transformations S and T can be analyzed by looking at extensions in which S and T are embedded in a two real variable flow. For a suitable class of extensions, the directional behavior observed is determined not by the extension itself, but by intrinsic spectral properties of the original action by S and T. Tuesday, September 25, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, September 25, 2012  Del Edit Copy Submitted by franklan.  David Gepner (Universität Regensburg)Brauer groups of commutative ring spectraAbstract: The Picard and Brauer groups of a commutative ring spectrum R can be interpreted as the first two negative homotopy groups of a nonconnective version of the spectrum of units of R. We'll focus on two techniques for computing these negative homotopy groups: if R is connective, then any Azumaya R-algebra is etale locally trivial, and these groups reduce to the etale cohomology of the sheaf of units$GL_1$; if R is nonconnective, then this probably fails, but nevertheless R often admits interesting finite G-Galois extensions whose group cohomology computes the relative Picard and Brauer groups. This is joint work with B. Antieau and T. Lawson, respectively. Probability Seminar 2:00 pm in 347 Altgeld Hall, Tuesday, September 25, 2012  Del Edit Copy Submitted by kkirkpat.  Fabrice Baudoin [email] (Purdue Math)Some aspects of stochastic differential equations driven by fractional Brownian motionsAbstract: In this talk we will review several results on stochastic differential equations driven by fractional Brownian motions that the speakers obtained in a series of more or less recent works. We shall in particular focus on the study of gradients bounds, Gaussian heat kernels bounds and small time asymptotics for the operators naturally associated with such equations. The presentation will be based on joint works with L. Coutin, M. Hairer, C. Ouyang and S. Tindel. Algebra, Geometry and Combinatorics 2:00 pm in 345 Altgeld Hall, Tuesday, September 25, 2012  Del Edit Copy Submitted by bwyser.  Michael Joyce [email] (Tulane University)Type A Symmetric Varieties and Schubert PolynomialsAbstract: Symmetric varieties, such as the variety which parameterizes smooth quadric hypersurfaces in a projective space, admit decompositions into orbits of a Borel subgroup, analogous to the Schubert cell decomposition of Grassmannians and flag varieties. Studying the analogue of the weak order for these varieties leads to interesting poset structures on the sets of involutions, fixed point free involutions, certain signed involutions, and some further variants of these objects. We explicitly describe the maximal chains in these posets and use the calculations to provide interesting factorizations of certain multiplicity-free sums of Schubert polynomials. This is joint work with Mahir Can and Ben Wyser. Algebraic Geometry Seminar 3:00 pm in 243 Altgeld Hall, Tuesday, September 25, 2012  Del Edit Copy Submitted by katz.  Sheldon Katz (Illinois Math)Refined Stable Pair Invariants on Local Calabi-Yau ThreefoldsAbstract: A refinement of the stable pair invariants of Pandharipande and Thomas is introduced, either as an application of the equivariant index recently introduced by Nekrasov and Okounkov or as "motivic" Laurent polynomial based on what we call the virtual Bialynicki-Birula decomposition, specializing to the usual stable pair invariants. We propose a product formula for the refined invariants extending the motivic product formula of Morrison, Mozgovoy, Nagao, and Szendroi for local$P^1$, based on the refined BPS invariants of the string theorists Huang, Kashani-Poor, and Klemm. We explicitly compute the invariants in low degree for local$P^2$and local$P^1 \times P^1$and check that they agree with the predictions of string theory and with our conjectured product formula. This is joint work with Jinwon Choi and Albrecht Klemm. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, September 25, 2012  Del Edit Copy Submitted by lidicky.  Cory Palmer [email] (UIUC Math)On the tree-packing conjectureAbstract: The tree packing conjecture of Gyárfás states that any set of$n-1$trees on$n,n-1,\dots, 2$vertices pack into$K_n$. For large$n$we prove that$t=\frac{1}{4}n^{1/3}$trees on$n,n-1,\dots, n-t+1$vertices pack into$K_n$as long as each tree has maximum degree at least$n^{2/3}$. This complements a corollary of a Theorem of Komlós, Sárközy and Szemerédi that for large$n$we can pack$t=\omega(\log n)$trees of maximum degree at most$\frac{n}{3t}$into$K_n$. Furthermore, we show that$t=\frac{1}{10}n^{1/4}$trees on$n,n-1,\dots, n-t+1$vertices pack into$K_{n+1}$(for$n$large enough). This is joint work with Jószef Balogh. Wednesday, September 26, 2012 IMSE Brown Bag Lunch Seminar 12:00 pm in 170 Everitt Hall, Wednesday, September 26, 2012  Del Edit Copy Submitted by katz.  Presenters: Luke Olson, Iwan Duursma, and Olgica Milenkovic (Illinois Computer Science, Mathematics, and Electrical & Computer Engineering)To Be Announced Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, September 26, 2012  Del Edit Copy Submitted by laugesen.  Ely Kerman [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Hamiltonian dynamical systems and their periodic orbits Abstract: In this talk I will introduce the notion of a Hamiltonian dynamical system and discuss several theorems and open problems concerning their periodic orbits. We will start with basic examples from classical mechanics and a beautiful theorem of Henri Poincare, and will work our way up to problems at the forefront of current research activity. Thursday, September 27, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, September 27, 2012  Del Edit Copy Submitted by ford.  Armin Straub (UIUC Math)Arithmetic aspects of short random walksAbstract: We revisit a classical problem: how far does a random walk travel in a given number of steps (of length 1, each taken along a uniformly random direction)? Although such random walks are asymptotically well understood, surprisingly little is known about the exact distribution of the distance after just a few steps. For instance, the average distance after two steps is (trivially) given by$4/\pi$; but what is the average distance after three steps? In this talk, we therefore focus on the arithmetic properties of short random walks and consider both the moments of the distribution of these distances as well as the corresponding density functions. It turns out that the even moments have a rich combinatorial structure which we exploit to obtain analytic information. In particular, we find that in the case of three and four steps, the density functions can be put in hypergeometric form and may be parametrized by modular functions. Much less is known for the density in case of five random steps, but using the modularity of the four-step case we are able to deduce its exact behaviour near zero. Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, September 27, 2012  Del Edit Copy Submitted by katz.  Mike Stone (Illinois Physics)Hawking radiation in the Quantum Hall effect: special functions in Bargmann-Fock spaceAbstract: I use the identification of the edge mode of the filling fraction$\nu=1$quantum Hall phase with a 1+1 dimensional chiral Dirac fermion to construct an analogue model for a chiral fermion in a space-time geometry possessing an event horizon. By solving the model in the lowest Landau level, I show that the event horizon emits particles and holes with a thermal spectrum. The solution involves some classical hypergeometric function theory in Bargmann-Fock space. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, September 27, 2012  Del Edit Copy Submitted by collier3.  Bill Karr (UIUC Math)Geodesics on Surfaces of Revolution in Minkowski SpaceAbstract: I will introduce some basic definitions from Lorentzian geometry and a notion of angle in the tangent space to a Lorentzian manifold. Then, I'll explain my REGS project about geodesics on surfaces of revolution in Minkowski space using a spacetime version Clairaut's relation from classical differential geometry. Applied Mathematics Seminar 3:00 pm in 241 Altgeld Hall, Thursday, September 27, 2012  Del Edit Copy Submitted by rdeville.  Maxim Arnold (UIUC Math)Evolution of the shape of asymptotic convex hull of the rapidly exploring random treeAbstract: Rapidly exploring Random Trees (RRT) have become increasingly popular as a way to explore high-dimensional spaces for problems in robotics, motion planning, virtual prototyping, computational biology, and other fields. It was established that the vertex distribution converges in probability to the sampling distribution. It was also noted that there is a "Voronoi bias" in the tree growth because the probability that a vertex is selected is proportional to the volume of its Voronoi region. I shall explain the evolution of the shape of convex hull of RRT when the size of the search space is increased. Commutative Ring Theory 3:00 pm in 243 Altgeld Hall, Thursday, September 27, 2012  Del Edit Copy Submitted by s-dutta.  Sankar Dutta (UIUC Math)The Monomial Conjecture and Order IdealsAbstract: In this talk we will show that a special case of the order ideal conjecture, originating from Evans and Griffiths' work in equicharacteristic, implies the monomial conjecture due to Hochster. We will derive a necessary and sufficient condition for this special case to be valid in terms of certain syzygies of canonical modules possessing free summands. We will also discuss two particular cases where the above condition holds good. Mathematics Colloquium 4:00 pm in 245 Altgeld Hall, Thursday, September 27, 2012  Del Edit Copy Submitted by kapovich.  Alessio Figalli (University of Texas - Austin)Stability results for functional inequalities and applicationsAbstract: Geometric and functional inequalities play a crucial role in several problems arising in the calculus of variations, partial differential equations, geometry, etc. More recently, there has been a growing interest in studying the stability for such inequalities. The basic question one wants to address is the following: suppose we are given a functional inequality for which minimizers are known. Can we prove that if a function almost attains the equality then it is close (in some suitable sense) to one of the minimizers? The aim of this talk is to describe some ways to attack this kind of problems, and to show some applications. The talk is intended to be accessible to graduate students. Illinois Geometry Lab 5:00 pm in 102 Altgeld Hall, Thursday, September 27, 2012  Del Edit Copy Submitted by lukyane2.  Jonathan Manton (UIUC Math)3D Printer TutorialAbstract: A tutorial on the use of the Makerbot Replicator for IGL members. Department members are welcome to attend. Friday, September 28, 2012 Model Theory and Descriptive Set Theory Seminar 3:00 pm in 347 Altgeld Hall, Friday, September 28, 2012  Del Edit Copy Submitted by phierony.  Aristotelis Panagiotopoulos (UIUC Math)Unitary representations of oligomorphic groupsAbstract: We will discuss the paper "Unitary representations of oligomorphic groups" by T. Tsankov (GAFA, (2) 22 (2012), 528-555). This will be the second talk of a series about this paper. Monday, October 1, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall , Monday, October 1, 2012  Del Edit Copy Submitted by mbrannan.  Wan-Yu Wu (UIUC Math)Projections in von Neumann algebras, Part IAbstract: We will discuss the type-classification of projections in von Neumann algebras. Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, October 1, 2012  Del Edit Copy Submitted by fcellaro.  Joseph Vandehey (UIUC)When T-normality equals S-normalityAbstract: Determining whether a point is normal for a given transformation T is a very difficult problem, yet there are several results that state that being T-normal is the same as being S-normal for two different transformations T and S. For example if a number is base-2-normal then it must also be base-4-normal, and vice-versa. We will present some new investigations into this topic, including a relation between normality for regular continued fractions and odd continued fractions. This will be an informal talk based on work in progress. Tuesday, October 2, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, October 2, 2012  Del Edit Copy Submitted by franklan.  Inna Zakharevich (University of Chicago)Ring structures on scissors congruence spectraAbstract: Hilbert's third problem asks the following question: given two polyhedra, when is it possible to dissect them into a finite number of pairwise congruent polyhedra? The answer, given by the Dehn-Sydler theorem (1901,1965) is that it is possible whenever two invariants -- the volume and the Dehn invariant -- are equal. Generalizing this problem, we can say that two polytopes in a nice enough manifold (such as$R^n$,$S^n$, or$H^n$) are "scissors congruent" if they can be dissected into a finite number of pairwise congruent polytopes and ask for a classification of scissors congruence types. This question was studied by Dupont and Sah, who assigned groups of scissors congruence types on manifolds and analyzed many structures on these groups. In particular, it turns out that in the case of$E^n$and$S^n$, the groups assemble into a graded ring. In this talk we give a different perspective on scissors congruence groups by showing that they arise as the 0-th K-group of a particular type of Waldhausen category, and use Dupont and Sah's observations to construct these ring structures directly on the K-theoretic level. Geometry Semiinar 2:00 pm in 243 Altgeld Hall, Tuesday, October 2, 2012  Del Edit Copy Submitted by sba.  Yuriy Mileyko (UIUC )Reincarnations in persistent homology with application to shape skeletaAbstract: The theory of persistent homology relies heavily on the existence of birth-death decompositions of persistence modules. The latter are sequences of vector spaces (indexed by integers or real numbers) connected by linear maps. It is important to note that the existence the birth-death decomposition is indifferent to the fact that a persistence module typically represents the (co)homology of a sequence of nested spaces, which is often obtained by using excursion sets of a continuous function. In this talk we show that by employing exact sequences and cap/cup products in homology and cohomology we can create an additional structure on top of the birth-death decompositions which relates deaths of (co)homology in one dimension with births in a different dimensions. This leads to the concept of a reincarnation. We show that reincarnations can be very useful when studying excursion sets of a family of functions. In particular, we use reincarnations to provide an alternative definition of the medial axis, curve skeleton, and even higher order skeleta. Algebra, Geometry and Combinatorics 2:00 pm in 345 Altgeld Hall, Tuesday, October 2, 2012  Del Edit Copy Submitted by bwyser.  Xiaoguang Ma [email] (UIUC Math)Torus knot invariants and Macdonald polynomialsAbstract: In arXiv:1111.6195, I. Cherednik gave a new 2-parameter invariants for torus knots by using double affine Hecke algebras and Macdonald polynomials. In this talk, I will first recall the basic theory about knot invariants. Then I will explain Cherednik's construction in the easiest case: A_1 and give an elementary proof in this simple case. Algebraic Geometry Seminar 3:00 pm in 243 Altgeld Hall, Tuesday, October 2, 2012  Del Edit Copy Submitted by choi29.  Gabriele La Nave (UIUC Math)Abramovich-Vistoli vs. Alexeev/Kollar--Shepherd-BarronAbstract: I will discuss why Kontsevich stable maps into DM stacks are stacky in nature and discuss Abramovich-Vistoli's theory of twisted curves and their consequent description of the compactification of the moduli space of "fibered surfaces" in contrast with Kollar--Shepherd-Barron MMP type of compactifications. I will then describe how to use these tools along with some toric geometry to give complete explicit description of the boundary of the moduli space of elliptic surfaces with sections. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, October 2, 2012  Del Edit Copy Submitted by lidicky.  Elyse Yeager [email] (UIUC Math)A Refinement of the Corrádi-Hajnal TheoremAbstract: In 1963, Corrádi and Hajnal proved the following result: If a graph$G$has$|V(G)| \geq 3k$and$\delta(G) \geq 2k$for some$k$, then$G$has$k$vertex-disjoint cycles. Clearly, the bound$n \geq 3k$is sharp. The minimum degree is also sharp, as evidenced by the join of$K_{2k-1}$and an independent set. Enomoto and Wang independently proved that the theorem still holds if the weaker requirement$\sigma_2(G) \geq 4k-1$replaces$\delta(G) \geq 2k$. Using the method from Enomoto's paper, we prove the following: If a graph$G$has$|V(G)| \geq 3k+1$and$\sigma_2(G) \geq 4k-2$and$G$does not have$k$disjoint cycles, then$\alpha(G) \geq |V(G)|-2k+1$. This is joint work with Hal Kierstead and Alexandr Kostochka. Job Application Workshop 4:30 pm in 245 Altgeld Hall, Tuesday, October 2, 2012  Del Edit Copy Submitted by funk3.  Kelly Yancey and Others (UIUC Math)Application MaterialsAbstract: Our AWM chapter will be sponsoring the first Job Application Workshop of the semester. Recently I attended a Career Mentoring Workshop at Wheaton College for women in mathematics who are in their last year. I would like to share with everyone what I learned. I will talk about what materials go into an application and the details about what goes into a cover letter, CV, research statement, and teaching statement. Also, Karen Mortensen and hopefully Rick Laugesen will be there to share their advice. Wednesday, October 3, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Wednesday, October 3, 2012  Del Edit Copy Submitted by mbrannan.  Wan-Yu Wu (UIUC Math)Projections in von Neumann algebras, Part IIAbstract: A continuation from Monday's lecture. Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, October 3, 2012  Del Edit Copy Submitted by laugesen.  Florin Boca [email] (UIUC Math)Angular distribution of lattices points and related geometric probability problemsAbstract: We will discuss some problems arising from the study of various discrete periodic configurations of points in Euclidean or Hyperbolic spaces. The associated distribution of angles is of particular interest to us. Ideas and methods from Number Theory, Ergodic Theory and Dynamical Systems that play an important role in the study of this kind of problems will be outlined. Thursday, October 4, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, October 4, 2012  Del Edit Copy Submitted by ford.  Ken Stolarsky (UIUC Math)Distribution mod 1: three points of view Abstract: Three areas that connect with distribution of sequences mod 1 are number theory, numerical integration, and approximation theory. The most important reference here is the classic book of Kuipers and Niederreiter. Now a "new" framework based on reproducing kernels may become prominent. We outline this, examine the one-dimensional setting, and briefly indicate how it impacts higher dimensional distributions. This material has been gleaned from papers of J. Brauchat, J. Dick, F. Hickernell, and F. Pillichshammer. This talk is intended to be accessible to first year graduate students. Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, October 4, 2012  Del Edit Copy Submitted by katz.  Sheldon Katz (Illinois Math)Superspace and supersymmetryAbstract: In this talk, I will formulate supersymmetry as a geometric symmetry, using the language of supermanifolds. Examples will be given. This talk can be understood independent of my recent talk on supermanifolds and Berezin integration. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, October 4, 2012  Del Edit Copy Submitted by collier3.  Sarah Yeakel (UIUC Math)What is Calculus of Functors?Abstract: Functors between categories give a wealth of information, but can be extremely complicated to compute. We teach our calculus students to approximate difficult real valued functions with polynomials. This technique can be applied to categories we know and love to produce some awesome results. I'll talk about some basic examples of functors on topological spaces and how the theory can be used on manifolds and vector spaces as well. Commutative Ring Theory 3:00 pm in Altgeld Hall, Thursday, October 4, 2012  Del Edit Copy Submitted by s-dutta.  Sankar Dutta (UIUC Math)On modules of finite projective dimensionAbstract: In this talk first we would point out the relation between the Monomial conjecture and Serre's conjectures on intersection multiplicities. Next a solution to the imbedding problem for modules of finite projective dimension will be presented followed by a special case of the order ideal conjecture. Mathematics Colloquium 4:00 pm Thursday, October 4, 2012  Del Edit Copy Submitted by kapovich.  Talk Cancelled for Today Friday, October 5, 2012 Model Theory and Descriptive Set Theory Seminar 3:00 pm in 347 Altgeld Hall, Friday, October 5, 2012  Del Edit Copy Submitted by phierony.  Slawomir Solecki (UIUC Math)Unitary representations of oligomorphic groupsAbstract: We will discuss the paper "Unitary representations of oligomorphic groups" by T. Tsankov (GAFA, (2) 22 (2012), 528-555). This will be the third talk of a series about this paper. Monday, October 8, 2012 Operator Algebra Learning Seminar 10:00 am in Altgeld Hall, Monday, October 8, 2012  Del Edit Copy Submitted by mbrannan.  Qiang Zeng (UIUC Math)Projections in Von Neumann Algebras, IV Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, October 8, 2012  Del Edit Copy Submitted by fcellaro.  Joseph Rosenblatt (UIUC)Optimal Norm Approximation in Ergodic TheoryAbstract: Classical ergodic averages give norm approximations but these averages are usually not the best one can do among all possible averages. We consider what the optimal approximation can be in terms of the transformation and the function. Tuesday, October 9, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, October 9, 2012  Del Edit Copy Submitted by franklan.  Marc Hoyois (Northwestern University)From algebraic cobordism to motivic cohomologyAbstract: I will present a famous theorem due to Hopkins and Morel which characterizes motivic cohomology of schemes as the universal oriented cohomology theory with additive formal group law. The talk will serve as a gentle introduction to motivic homotopy theory, geared towards understanding the statement of the theorem and some of its stunning applications. Probability Seminar 2:00 pm in Altgeld Hall 347, Tuesday, October 9, 2012  Del Edit Copy Submitted by kkirkpat.  Sebastien Roch (U Wisconsin-Madison)Probabilistic Techniques in Mathematical Phylogenetics: Relating Combinatorial and Variational Distances on TreesAbstract: I will describe recent results on a connection between the so-called reconstruction problem on Markov random fields on trees and two important problems in computational evolutionary biology: the inference of ancestral states and the estimation of phylogenies using maximum likelihood. This is joint work with Allan Sly. No biology background will be assumed. Algebra, Geometry and Combinatorics 2:00 pm in 345 Altgeld Hall, Tuesday, October 9, 2012  Del Edit Copy Submitted by bwyser.  Javid Validashti [email] (UIUC Math)A hands-on approach to tensor product surfacesAbstract: A central problem in geometric modeling is to find the implicit equations for a curve or surface defined by a regular or rational map. In a joint work with H. Schenck and A. Seceleanu we classify all possible minimal free resolutions of the ideal associated to a tensor product surface$S$of bidegree$(2,1)$in$\mathbb{P}^3$, which allows us to use the method of approximation complexes to determine the implicit equation of$S$. Algebraic Geometry Seminar 3:00 pm in 243 Altgeld Hall, Tuesday, October 9, 2012  Del Edit Copy Submitted by katz.  David Smyth (Harvard)Stability of finite Hilbert pointsAbstract: The classical construction of the moduli space of stable curves via Geometric Invariant Theory relies on the asymptotic stability result of Gieseker and Mumford that the m-th Hilbert Point of a pluricanonically embedded curve is GIT-stable for all sufficiently large m. Several years ago, Hassett and Keel observed that if one could carry out the GIT construction with non-asymptotic linearizations, the resulting models could be used to run a log minimal model program for the space of stable curves. A fundamental obstacle to carrying out this program has been the absence of a non-asymptotic analogue of Gieseker's stability result, i.e. how can one prove stability of the m-th Hilbert point for small values of m? In recent work with Jarod Alper and Maksym Fedorchuk, we prove that the the m-th Hilbert point of a general smooth canonically or bicanonically embedded curve is GIT-semistabe for all m>1. For (bi)canonically embedded curves, we recover Gieseker-Mumford stability by a much simpler proof. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, October 9, 2012  Del Edit Copy Submitted by lidicky.  Hal Kierstead [email] (Arizona State University)On directed versions of the Corrádi-Hajnal CorollaryAbstract: For$k\in \mathbb N$, the Corrádi-Hajnal Corollary states that every graph$G$on$3k$vertices with minimum degree$\delta(G)\ge2k$has a$C_3$-factor, i.e., a partitioning of the vertex set so that each part induces the$3$-cycle$C_3$. I will discuss directed versions of the Corr\'adi-Hajnal Corollary in terms of both minimum total degree$\delta_t(\overrightarrow G):=\min_{v\in V}(deg^-(v)+deg^+(v))$and minimum semidegree$\delta_0(\overrightarrow G):=\min_{v\in V}\{deg^-(v),deg^+(v)\}$. Wednesday, October 10, 2012 Operator Algebra Learning Seminar 10:00 am in Altgeld Hall, Wednesday, October 10, 2012  Del Edit Copy Submitted by mbrannan.  Qiang Zeng (UIUC Math)Projections in Von Neumann Algebras,VAbstract: We will finish our discussion of projections and type-classification for von Neumann algebras. Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, October 10, 2012  Del Edit Copy Submitted by laugesen.  Rui Fernandes (Department of Mathematics, University of Illinois at Urbana-Champaign)What is Poisson geometry?Abstract: Poisson Geometry is an amalgam of three classical theories: (it is) Foliation Theory (inside which) Symplectic Geometry and Lie Theory (interact with each other). In this talk I will explain how Poisson geometry grew out of classical mechanics and discuss some of its modern developments and open problems. Thursday, October 11, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, October 11, 2012  Del Edit Copy Submitted by ford.  Amanda Folsom (Yale Math)q-series and quantum modular formsAbstract: While the theory of mock modular forms has seen great advances in the last decade, questions remain. We revisit Ramanujan's last letter to Hardy, and prove one of his remaining conjectures as a special case of a more general result. Surprisingly, the rank function, crank function, mock theta functions, and quantum modular forms, all play key roles. This is joint work with K. Ono (Emory U.) and R.C. Rhoades (Stanford U.). Logic Seminar 1:00 pm in 243 Altgeld Hall, Thursday, October 11, 2012  Del Edit Copy Submitted by ssolecki.  Marcin Sabok (Polish Academy of Sciences)Canonization for equivalence relations classifiable by countable structuresAbstract: I will discuss several results on canonical Ramsey theory in the context of descriptive set theory. I will focus on Borel equivalence relations which are classifiable by countable structures and show what kind of canonization results can be obtained for this class. Canonization in this class will turn out to be closely related to canonization in the smaller class of essentially countable equivalence relations. Group Theory 1:00 pm in 347 Altgeld Hall, Thursday, October 11, 2012  Del Edit Copy Submitted by nmd.  Bo Gwang Jeon (UIUC)Number fields associated to hyperbolic 3-manifoldsAbstract: In the studies of hyperbolic 3-manifolds, the following question is natural: "For an n-cusped manifold M and a constant D>0, are there finitely many Dehn fillings of M whose trace fields have degree< D?" Although it is commonly believed that the answer is yes and Hodgson proved it for the 1-cusped case, little was previously known in general. In the talk, I'll discuss some further steps to answer the question. Special Representation Theory Seminar 2:00 pm in 345 Altgeld Hall, Thursday, October 11, 2012  Del Edit Copy Submitted by nevins.  Chris Dodd (University of Toronto)Modules over Algebraic Quantizations and representation theoryAbstract: Recently, there has been a great deal of interest in the theory of modules over algebraic quantizations of so-called symplectic resolutions. In this talk I'll discuss some new work -joint, and very much in progress- that open the door to giving a geometric description to certain categories of such modules; generalizing classical theorems of Kashiwara and Bernstein in the case of D-modules on an algebraic variety. Graduate Geometry Topology Seminar 2:00 pm in Altgeld Hall, Thursday, October 11, 2012  Del Edit Copy Submitted by collier3.  Mychael Sanchez (UIUC Math)Homotopy theory and infinity categoriesAbstract: I'll talk about several objects of interest in homotopy theory, some properties they share, and some deficiencies of ordinary category theory when studying them. I'll then discuss a class of mathematical objects called infinity categories that correct some these deficiencies and how we might come up with them. Groupoids and Stacks 3:00 pm in 345 Altgeld Hall, Thursday, October 11, 2012  Del Edit Copy Submitted by lerman.  Rui Fernandes (UIUC Math)Introduction to Lie groupoidsAbstract: Introduction to Lie groupoids Commutative Ring Theory Seminar 3:00 pm in 243 Altgeld Hall, Thursday, October 11, 2012  Del Edit Copy Submitted by jvalidas.  Javid Validashti [email] (UIUC Math)Implicitization of Tensor Product SurfacesAbstract: I will discuss the construction of approximation complexes, introduced by Herzog, Simis and Vasconcelos, and their application in computing implicit equations of tensor product surfaces. This is a continuation of my last two talks on syzygies and singularities of tensor product surfaces based on a joint work with H. Schenck and S. Seceleanu. Mathematics Colloquium 4:00 pm in 245 Altgeld Hall, Thursday, October 11, 2012  Del Edit Copy Submitted by kapovich.  Jayce Getz (Duke University)An introduction to Langlands functorialityAbstract: We introduce Langlands functoriality. Special attention is taken to explain why the functoriality conjecture is natural even without considering analogies with the theory of Galois representations. Friday, October 12, 2012 Special Seminar 2:00 pm in 241 Altgeld Hall, Friday, October 12, 2012  Del Edit Copy Submitted by nmd.  Jordan Ellenberg (University of Wisconsin - Madison)New developments in homological stability and FI-modulesAbstract: In topology and algebraic geometry one often encounters phenomena of _stability_. A famous example is the cohomology of the moduli space of curves$M_g$; Harer proved in the 1980s that the sequence of vector spaces$H_i(M_g, \mathbb{Q})$, with$g$growing and$i$fixed, has dimension which is eventually constant as$g$grows with$i$fixed. In many similar situations one is presented with a sequence$\{V_n\}$, where the$V_n$are not merely vector spaces, but come with an action of$S_n$. In many such situations the dimension of$V_n$does not become constant as$n$grows -- but there is still a sense in which it is eventually "always the same representation of$S_n$" as n grows. The preprint http://arxiv.org/abs/1204.4533 shows how to interpret this kind of "representation stability" as a statement of finite generation in an appropriate category; we'll discuss this set-up and some applications to the topology of configuration spaces, the representation theory of the symmetric group, and diagonal coinvariant algebras. As a sample result, we explain how to show that the$i$th Betti number of the configuration space of$n$(ordered) points on a manifold$M$is, for large enough$n$, not constant, but rather a polynomial in$n$. This talk will be aimed at a broad audience at the level of a typical colloquium. (joint work with T. Church, B. Farb, and R. Nagpal) Logic Seminar 3:00 pm in 347 Altgeld Hall, Friday, October 12, 2012  Del Edit Copy Submitted by phierony.  Isaac Goldbring (UIC)The theory of tracial von Neumann algebras does not have a model companionAbstract: In this talk, we will show that the theory of tracial von Neumann algebras does not have a model companion. In addition, we will show that a positive solution to the Connes Embedding Problem implies that there is no model complete theory of tracial von Neumann algebras. All functional analytic notions and most model-theoretic notions will be defined. This is joint work with Bradd Hart and Thomas Sinclair. Monday, October 15, 2012 Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, October 15, 2012  Del Edit Copy Submitted by fcellaro.  Scott Kaschner (IUPUI)Superstable Manifolds of Invariant Circles and Co-dimension 1 Böttcher FunctionsAbstract: Let$f:X\dashrightarrow X$be a dominant meromorphic self-map, where$X$is a compact connected Hermitian manifold of dimension$n > 1$. Suppose there is an embedded copy of$\mathbb P^1$that is invariant under$f$, with$f$holomorphic and transversally superattracting with degree$a$in some neighborhood. Suppose also that f restricted to this line is given by$z\rightarrow z^b$, with resulting invariant circle$S$. The regularity of the local stable manifold$\mathcal W^s_{\scriptsize{loc}}(S)$is dependent on$a$and$b$. Specifically, I will show that when$a\geq b$,$\mathcal W^s_{\scriptsize{loc}}(S)$is real analytic, and the condition$a\geq b$cannot be relaxed without adding additional hypotheses. Tuesday, October 16, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Tuesday, October 16, 2012  Del Edit Copy Submitted by ford.  Bruce Berndt (UIUC Math)The circle problem, the divisor problem, and 109 years of Bessel series expansionsAbstract: After a brief description of the circle and divisor problems, we give a survey of Bessel series expansions that are associated with these problems. We discuss the contributions of Voronoi, Ramanujan-Hardy, and the speaker's work with Sun Kin and Alexandru Zaharescu. Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, October 16, 2012  Del Edit Copy Submitted by franklan.  Anthony Elmendorf (Purdue University Calumet)Generalized and equivariant multicategoriesAbstract: Leinster developed a general procedure for defining multicategories using monads satisfying a Cartesian property. However, his definition only captures the usual notion of multicategory in the case when the multicategory doesn't have a symmetric structure. By looking at additional structure available when we start with a general$\Sigma$-free operad in Cat, we can account for the symmetric structure, and thereby generalize Leinster's construction to this case. The construction also easily accounts for the sort of equivariant operads considered by Guillou, May, and Merling in their ongoing study of equivariant infinite loop space theory via equivariant permutative categories. There are several natural conjectures that we will discuss. Logic Seminar 1:00 pm in 345 Altgeld Hall, Tuesday, October 16, 2012  Del Edit Copy Submitted by ssolecki.  Dima Sinapova (UIC)The Singular Cardinal Problem and Prikry ForcingsAbstract: The Singular Cardinal Problem is the problem to completely describe the behavior of the operation$\kappa\mapsto 2^\kappa$restricted to singular cardinals. Dealing with this problem involves constructing various models where the Singular Cardinal Hypothesis (SCH) fails. This is done using Prikry type forcings in the context of large cardinals. I will give some background on the subject and then go over some resent consistency results about the relationship between SCH and weak square. Geometry Seminar 2:00 pm in 243 Altgeld Hall, Tuesday, October 16, 2012  Del Edit Copy Submitted by sba.  Kenneth Stolarsky (UIUC)Distance geometry, reproducing kernels, and numerical integrationAbstract: How should n points be placed on the surface of a d-dimensional sphere to minimize or maximize a given function of their mutual Euclidean distances? Some fundamental problems of numerical integration have recently been given a new framework based on the not so recent concept of reproducing kernels. It turns out that this framework provides new insights into distance geometry by viewing in a certain way the Euclidean distance between points as the essential part of a reproducing kernel. This talk will be based on work by J. Brauchart, J. Dick, F. Hickernell, and F. Pillichshammer. It will have significant overlap with the seminar given by the speaker on October 4. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, October 16, 2012  Del Edit Copy Submitted by lidicky.  Hong Liu (UIUC Math)Multicolor Ramsey Numbers for Triple SystemAbstract: We consider some general results on multicolor Ramsey number for three-uniform hypergraphs, as well as Ramsey numbers for specific hypergraphs. All of this work is very preliminary and we are just at the stage of exploring the general problem. This is joint work with Maria Axenovich, Roman Glebov, Dhruv Mubayi and András Gyárfás Wednesday, October 17, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Wednesday, October 17, 2012  Del Edit Copy Submitted by mbrannan.  Stephen Longfield (UIUC Math)Completely Positive Maps Math 499 – REGS Day 4:00 pm in 245 Altgeld Hall, Wednesday, October 17, 2012  Del Edit Copy Submitted by seminar.  REGS Day 2012Abstract: On the basis of final reports submitted by eligible participants in the 2012 summer REGS program, three Fellows were selected to give short presentations on their projects. The talks will be held from 4–5 p.m. in 245 Altgeld Hall followed by a pizza party and awarding of prizes from 5:15–7:00 p.m. in the Common Room (321 Altgeld Hall). Presenters are: Nickolas Anderson, Hecke-type congruences for two smallest parts functions Abstract: We prove infinitely many congruences modulo$3$,$5$, and powers of$2$for the overpartition function$\overline{p}(n)$and two smallest parts functions:$\overline{\operatorname{spt1}}(n)$for overpartitions and$\operatorname{M2spt}(n)$for partitions without repeated odd parts. These resemble the Hecke-type congruences found by Atkin for the partition function$p(n)$in 1966 and Garvan for the smallest parts function$\operatorname{spt}(n)$in 2010. Erin Compaan, Sequences and Conserved Quantities via Cluster Algebras Abstract: In this talk, I will begin by presenting an introduction to sequences defined through cluster algebras with geometric coefficients. Under some conditions, these sequences exhibit conserved quantities. In these cases, the generating function of the sequence can be expressed in closed form.This result is generalized to a less restrictive class of cluster algebras. The generating function is then used to derive results about the asymptotic growth rate of the sequence. Xiumin Du, Orthogonal Polynomials and Discrete Toda EquationsAbstract: First we will show some relation between tri-diagonal Lax matrix for Toda lattice and$A_r~Q-$system. It turns out that the evolution of$A_r~Q-$system along diagonal lines corresponds on Toda side to discrete evolution of conditions for Lax matrix. There is a well known method which uses Gaussian decomposition to give a solution to Lax equation with continuous evolution. We will use orthogonal polynomials to prove an analogous relation for discrete evolution. Finally we will generalize the result to Lax matrix with more than three diagonals. Thursday, October 18, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, October 18, 2012  Del Edit Copy Submitted by ford.  Michael Filaseta (Univ. South Carolina Math.)49598666989151226098104244512918Abstract: If$p$is a prime with decimal representation$d_{n} d_{n-1} \dots d_{1} d_{0}$, then a theorem of A. Cohn implies that the polynomial$f(x) = d_{n} x^{n} + d_{n-1}x^{n-1} + \cdots + d_{1}x + d_{0}$is irreducible. One can view this result as following from the fact that if$g(x) \in \mathbb Z[x]$with$g(0) = 1$, then$g(x)$has a root in the disk$D = \{ z \in \mathbb C: |z| \le 1 \}$. On the other hand, that such a$g(x)$has a root in$D$has little to do with$g(x)$having integer coefficients. In this talk, we discuss a perhaps surprising result about the location of a zero of such a$g(x)$that makes use of its coefficients being in$\mathbb Z$and discuss the implications this has on generalizations of Cohn's theorem. A variety of open problems will be presented. This research is joint work with a former student, Sam Gross. Group Theory Seminar 1:00 pm in Altgeld Hall 347, Thursday, October 18, 2012  Del Edit Copy Submitted by kapovich.  Alex Furman (University of Illinois at Chicago)Classifying lattice envelopes for (many) countable groupsAbstract: Let$\Gamma$be a given countable group. What locally compact groups$G$contain a lattice (not necessarily uniform) isomorphic to$\Gamma$? In a joint work with Uri Bader and Roman Sauer we answer this question for a large class of groups including Gromov hyperbolic groups and many linear groups. The proofs use a range of facts including: recent work of Breuillard-Gelander on Tits alternative, works of Margulis on arithmeticity of lattices in semi-simple Lie groups, and a number of quasi-isometric rigidity results. Analysis Seminar 2:00 pm in 243 Altgeld Hall, Thursday, October 18, 2012  Del Edit Copy Submitted by aimo.  Raanan Schul (SUNY Stony Brook)Lipschitz Functions vs. ProjectionsAbstract: We discuss joint work with Jonas Azzam. All Lipschitz maps from$R^7$to$R^3$are orthogonal projections''. This is of course quite false as stated. It turns out however, that there is a surprising grain of truth in this statement. We show that all Lipschitz maps from$R^7$to$R^3$(with 3-dimensional image) can be precomposed with a map$g:R^7\to R^7$such that$f\circ g$will satisfy, when we write the domain as$R^4\times R^3$and restrict to$E$, a large portion of the domain, that$f\circ g$will be constant in the first coordinate and biLipschitz in the second coordinate. Geometrically speaking, the map$g$distorts$R^7$in a controlled manner, so that the fibers of$f$are straightened out. Our results are quantitative. The target space can be replaced by any metric space! The size of the set$E$on which behavior is good is an important part of the discussion and examples such as Kaufman's 1979 construction of a singular map$[0,1]^3$onto$[0,1]^2$are an important enemy. On route we will discuss a new extension theorem which is used to construct the bilipschitz map$g$, improving results of Jones (88) and David (88). In particular, if$g:R^7\to R^7$is a Lipschitz map, then it agrees with a globally defined biLipschitz map$\hat{g}:R^7\to R^7$on a large piece of the domain. This was previously known only by increasing the dimension of the target space of$\hat{g}$(David and Semmes, 91). Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, October 18, 2012  Del Edit Copy Submitted by collier3.  Seth Wolbert (UIUC Math)Stacks in Differential GeometryAbstract: A stack over the category of smooth manifolds is a structure that can be used to generalize the deconstructive (i.e., via restriction) and reconstructive (i.e.,via gluing) properties seen in fiber bundles. This talk is designed to give a gentle introduction to these structures and some of their nice properties. Given time, we will also discuss the stack of transport functors and how parallel transport induces an equivalence of categories between this stack and the stack of principal G-bundles with connections. Groupoids and Stacks 3:00 pm in 345 Altgeld Hall, Thursday, October 18, 2012  Del Edit Copy Submitted by lerman.  Rui Fernandes (UIUC Math)Introduction to Lie groupoids (continued)Abstract: More fun with Lie groupoids Commutative Ring Theory Seminar 3:00 pm in 243 Altgeld Hall, Thursday, October 18, 2012  Del Edit Copy Submitted by jvalidas.  Howard Osborn (UIUC Math)New facets of Kaehler DerivativesAbstract: If a commutative algebra over a field of characteristic zero is isomorphic to a function algebra with values in the field, and if the unit element is the only nonzero idempotent, then the universal Kaehler derivative annihilates only the elements that correspond to constant functions. This result is used to show that the cotangent spaces of the algebra are mutually isomorphic, and that such an algebra has the analog of a smooth atlas if and only if its Kaehler module is reflexive. Mathematics Colloquium 4:00 pm in Altgeld Hall 245, Thursday, October 18, 2012  Del Edit Copy Submitted by kapovich.  Alex Furman (University of Illinois at Chicago)Groups with good pedigrees, or superrigidity revisitedAbstract: In the 1970s G.A. Margulis proved that certain discrete subgroups (namely lattices) of such Lie groups as SL(3,R) have no linear representations except from the given imbedding. This phenomenon, known as superrigidity, has far reaching applications and has inspired a lot of research in such areas as geometry, dynamics, descriptive set theory, operator algebras etc. We shall try to explain the superrigidity of lattices and related groups by looking at some hidden symmetries (Weyl group) that they inherit from the ambient Lie group. The talk is based on a joint work with Uri Bader. Friday, October 19, 2012 Model Theory and Descriptive Set Theory Seminar 3:00 pm in 347 Altgeld Hall, Friday, October 19, 2012  Del Edit Copy Submitted by phierony.  Slawomir Solecki (UIUC Math)Unitary representations of oligomorphic groupsAbstract: We will discuss the paper "Unitary representations of oligomorphic groups" by T. Tsankov (GAFA, (2) 22 (2012), 528-555). This will be the forth talk of a series about this paper. Operator Algebra Seminar 4:00 pm in 147 Altgeld Hall, Friday, October 19, 2012  Del Edit Copy Submitted by liang41.  Ali Kavruk (UIUC Math)Operator system and Characterization of QWEPAbstract: This is a continuation of Monday's talk about operator system tensor product. Monday, October 22, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Monday, October 22, 2012  Del Edit Copy Submitted by mbrannan.  Stephen Longfield (UIUC Math)Completely Bounded Maps and Tensor Products of C* Algebras Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, October 22, 2012  Del Edit Copy Submitted by fcellaro.  Francesco Di Plinio (IUB)A discrete model for the Hilbert transform along a smooth vector field in the plane.Abstract: Given a Calderon-Zygmund convolution kernel on R, we study the correspondent maximal directional singular integral T_V along directions in a finite set V with N elements. This operator can be regarded as a discrete version of the Hilbert transform along a planar vector field, the object of a conjecture of Stein, which in turn is related to differentiation along smooth vector fields. We are interested in the sharp dependence on N of the L^p and weak L^2 norms of T_V. We prove sharp bounds for both lacunary and Vargas sets of directions. The former case answers a question posed by M. Lacey. The latter includes uniformly distributed directions and the finite truncations of the Cantor set. This partially answers a conjecture of J. Kim. We make use of both classical harmonic analysis methods and new product-BMO based time-frequency analysis techniques, which could further prove useful in the study of multilinear multiparameter operators with modulation symmetry and of the conjectures of Zygmund and Stein. Joint work with Ciprian Demeter. Tuesday, October 23, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, October 23, 2012  Del Edit Copy Submitted by franklan.  Agnes Beaudry (Northwestern University)The K(2)-local Moore spectrum at the prime 2Abstract: We use methods of Goerss, Henn, Karamanov, Mahowald, and Rezk to study the homotopy$\pi_*L_{K(2)}V(0)$at the prime 2. In particular, we study the$E_2$-page of an Adams-Novikov spectral sequence converging to$\pi_*L_{K(2)}V(0)$via another spectral sequence called the short resolution spectral sequence. Its$E_1$-page is composed of cohomology groups$H^n(G_k, (E_2)_*V(0))$where$(E_2)_*$is Morava$E$-theory and the$G_k$'s are finite subgroups of the Morava stabilizer group$\mathbb{G}_2$. These finite groups come from automorphisms of elliptic curves and we use the geometry thus made available to us to simplify computations. We explain how to obtain the$E_2$-page of the short resolution spectral sequence for$(E_2)_*V(0)$and compute the complete spectral sequence for$v_1^{-1}(E_2)_*V(0)$. This gives the$E_2$-page of the Adams-Novikov spectral sequence, namely$H^*(\mathbb{G}_2, v_1^{-1}(E_2)_*V(0))$. We expect the differentials to follow classical patterns and explain what this would imply for$v_1^{-1}\pi_*L_{K(2)}V(0)$. Logic Seminar 1:00 pm in UIC, SEO 636, Tuesday, October 23, 2012  Del Edit Copy Submitted by phierony.  Midwest Model Theory DayAbstract: Midwest Model Theory Day at UIC. The speakers are Lynn Scow, Isaac Goldbring and Maryanthe Malliaris. For details, see http://www.math.wisc.edu/~andrews/MWMTD5.html Differential Geometry 1:00 pm in 243 Altgeld Hall, Tuesday, October 23, 2012  Del Edit Copy Submitted by lanave.  Gabriele La Nave (UIUC Math)Macroscopic dimension and fundamental groups of manifolds with positive isotropic curvature.Abstract: There is a long history in Comparison Geometry of drawing topological consequences from curvature properties. This usually involves studying consequences of curvature signs on either the nature of geodesics or the (non) existence of harmonic sections of special bundles. Micallef and Moore, around the late 80's, introduced the notion of manifolds with positive isotropic curvature --a notion of curvature which stems from complexifying the tangent bundle and its metric and which lies between positive sectional curvature and positive scalar curvature-- because best suited to the study of manifolds via the use of their minimal surfaces. Gromov introduced the notion of macroscopic dimension exactly to study questions related to the geometry/topology of manifolds with some sort of positive curvature and such notion turns out to be very useful in studying the topology of manifolds, especially in regards to questions pertaining the fundamental group. In the talk I will show how recent techniques of Donaldson's can be brought to bear in the study of the macroscopic dimension of manifolds with (uniformly) positive isotropic curvature Probability Seminar 2:00 pm in 347 Altgeld Hall, Tuesday, October 23, 2012  Del Edit Copy Submitted by kkirkpat.  Yan-Xia Ren (Peking University)A Strong Law of Large Numbers for Super-stable ProcessesAbstract: Let$X=(X_t, t\ge 0; P_\mu)$be a supercritical, super-stable process corresponding to the operator$-\left(-\Delta\right)^{\alpha/2 } u+\beta u-\eta u^2$on$\mathbb{R}^d$with constants$\beta,\eta>0$and$\alpha\in(0,2]$, and let$\ell $be Lebesgue measure on$\mathbb{R}^d$. Put$\hat W_t(\theta)=e^{(\beta-|\theta|^\alpha)t}X_t(e^{i\theta\cdot})$, which is a complex-valued martingale for each$\theta\in\mathbb{R}^d$with limit$\hat W(\theta)$say. Our main result establishes that for any starting measure$\mu$, which is a finite measure on$\mathbb{R}^d$such that$\int_{\mathbb{R}^d}x\mu(\mathrm{d}x)<\infty$,$ \frac{t^{d/\alpha}X_{t}}{e^{\beta t}}\rightarrow c_{\alpha }\hat W\left(0\right) \ellP_\mu$-a.s. in a topology, termed the shallow topology, strictly stronger than the vague topology yet weaker than the weak topology. This result can be thought of as an extension to a class of superprocesses of Watanabe's strong law of large numbers for branching Markov processes. This talk is based on a joint work with Michael A. Kouritzin. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, October 23, 2012  Del Edit Copy Submitted by lidicky.  John Lenz [email] (University of Illinois at Chicago)Quasirandom HypergraphsAbstract: Quasirandom or pseudorandom graphs, first studied by Thomason and shortly thereafter by Chung-Graham-Wilson, are graphs which behave like the random graph. Quasirandom graphs have many diverse applications throughout combinatorics and computer science and have emerged as an interesting object of study in their own right. In this talk, I will give an overview of our recent work on hypergraph quasirandomness and discuss as an application a polynomial-time strong refutation algorithm for random k-SAT. Joint work with Dhruv Mubayi. Wednesday, October 24, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Wednesday, October 24, 2012  Del Edit Copy Submitted by mbrannan.  Stephen Longfield (UIUC Math)Completely Bounded Maps and Tensor Products of C* Algebras, Part II Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, October 24, 2012  Del Edit Copy Submitted by laugesen.  Ilya Kapovich [email] (UIUC Math)Groups as geometric objectsAbstract: Geometric group theory is a vibrant and rapidly developing area of mathematics that lies at the juncture of group theory, low-dimensional topology, differential geometry and several other subjects. A crucial idea in the area is to view a finitely generated group as a geometric and not just as an algebraic object. One of the key tools for realizing this goal is the notion of the Cayley graph of a group, which is a metric space associated to a finitely generated group together with a finite generating set. Geometric group theory studies the connections between large-scale geometric properties of groups on one side and their algebraic and algorithmic properties on the other side. In this introductory talk we will explore the basic ideas and notions of the subject and demonstrate how the above connections manifest themselves in a number of representative results. Thursday, October 25, 2012 Department of Mathematics Retiree's Luncheon 11:30 am in Urbana Country Club, Thursday, October 25, 2012  Del Edit Copy Submitted by seminar. Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, October 25, 2012  Del Edit Copy Submitted by katz.  Marius Junge (Illinois Math)Non-locality from a math perspectiveAbstract: We discuss several ways to measure how a bipartite state can be used to perform non-local experiments. Traditionally, the entropy of entanglement is considered as such a measure. A more recent approach consists on constructing Bell-type inequalities as a witness of non-locality. The mathematical results will show that certain states are non-local in a very robust sense. If time allows we will describe recent results of Palazuelos, formerly a postdoc at UIUC, on superactivation of non-locality. Group Theory Seminar 1:00 pm Thursday, October 25, 2012  Del Edit Copy Submitted by kapovich.  No seminar today, because of the departmental retiree's luncheon Analysis Seminar 2:00 pm in 243 Altgeld Hall, Thursday, October 25, 2012  Del Edit Copy Submitted by aimo.  Valentino Magnani (University of Pisa, Italy)On the sub-Riemannian measure of submanifoldsAbstract: We present an explicit formula for the sub-Riemannian measure of a submanifold, embedded in a fixed stratified group. We show that in many cases this measure is equivalent to the Hausdorff measure of the submanifold with respect to the sub-Riemannian distance of the group. We discuss the important class of transversal submanifolds, for which the equivalence between Hausdorff measure and sub-Riemannian measure holds. This result has been recently obtained in collaboration with Jeremy Tyson and Davide Vittone. Some open questions will be addressed. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, October 25, 2012  Del Edit Copy Submitted by collier3.  Nathan Rehfuss (UIUC MATH)The Unknot and Why You Should Care.Abstract: I plan to give a brief general overview of knot theory, followed by an exploration of the methods, challenges, and applications of the unknotting problem. Groupoids and Stacks 3:00 pm in 345 Altgeld Hall, Thursday, October 25, 2012  Del Edit Copy Submitted by lerman.  Eugene Lerman (UIUC Math)Orbifolds as groupoidsAbstract: An orbifold is some sort of a geometric object that looks locally as coordinate vector space with (or divided out by) an action of a finite group. Making sense of it precisely leads to different notions of orbifolds -- orbifolds as groupoids, orbifolds as stacks ... Friday, October 26, 2012 Model Theory and Descriptive Set Theory Seminar 3:00 pm in 347 Altgeld Hall, Friday, October 26, 2012  Del Edit Copy Submitted by phierony.  Slawek Solecki (UIUC Math)Unitary representations of oligomorphic groupsAbstract: We will discuss the paper "Unitary representations of oligomorphic groups" by T. Tsankov (GAFA, (2) 22 (2012), 528-555). This will be the fifth talk of a series about this paper. G4G - Gathering for Gardner 2012 at Urbana-Champaign 5:30 pm in 314 Altgeld Hall, Friday, October 26, 2012  Del Edit Copy Submitted by phierony.  Four Colors Su ffice & Other Math WondermentsAbstract: Come join Champaign-Urbana's celebration of the spirit of recreational mathematics and fun math puzzles, and the life of math and science writer Martin Gardner. The University of Illinois and Wolfram Research will host a series of short talks by more than a dozen local mathematicians and computer scientists at the occasion of Gardner's 98th birthday. This event is part of the worldwide event Gathering for Gardner: Celebration of Mind. It is free and open to members of the public of all ages - no math training required to enjoy the presentations! For more details, see http://www.math.uiuc.edu/~phierony/gardner12.html Monday, October 29, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Monday, October 29, 2012  Del Edit Copy Submitted by mbrannan.  Jian Liang (UIUC Math)Tensor Products of Operator Algebras, Part I Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, October 29, 2012  Del Edit Copy Submitted by fcellaro.  Javier Parcet (Instituto de Ciencias Matemáticas, Madrid)Twisted Hilbert Transforms and Classical Harmonic Analysis Tuesday, October 30, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, October 30, 2012  Del Edit Copy Submitted by franklan.  Matthew Thibault (University of Chicago)Finite simplicial complexes via pro-posetsAbstract: One has a pair of functors between finite topological spaces and finite simplicial complexes. Via this correspondence, McCord proves that finite topological spaces up to weak homotopy equivalence coincides with finite simplicial complexes up to homotopy equivalence. Since finite topological spaces coincide with finite posets, this allows one to convert problems in algebraic topology into problems in combinatorics. However, due to a dearth of maps in the category of finite spaces, one must enlarge this category in order to describe all homotopy classes of maps between (finite) simplicial complexes. In this talk, I will describe the homotopy category of finite simplicial complexes in terms of the category of pro-posets. Logic Seminar 1:00 pm in 345 Altgeld Hall, Tuesday, October 30, 2012  Del Edit Copy Submitted by ssolecki.  Min Zhao (UIUC )A self-dual Ramsey theorem for Spencer's space and an abstract approach to Ramsey theoryAbstract: First, we will discuss the abstract approach to Ramsey theory and the self-dual Ramsey theorem for partitions developed by Solecki. Then we will introduce the Ramsey theorem for Spencer's space developed by Spencer. After that, by applying the abstract approach, we will give a self-dual Ramsey theorem for Spencer's spaces, which is a generalization of the self-dual Ramsey theorem for partitions. Geometry Seminar 2:00 pm in 243 Altgeld Hall, Tuesday, October 30, 2012  Del Edit Copy Submitted by sba.  Matthew Wright (Huntington University)Hadwiger Integration of Random FieldsAbstract: Hadwiger integrals provide various notions of the "size" of a function, analogous to the notions of size that the intrinsic volumes provide for a set. A random field is a stochastic process that we can think of as a random function; its value at each point its domain is a random variable. We can combine these concepts to consider the Hadwiger integrals of a random field. In this talk, I will provide some necessary background information about Hadwiger integrals and random fields. I will then compute the expected Hadwiger integrals of a family of random fields known as Gaussian-related random fields. These random fields have possible applications in sensor networks, signal processing, and other areas. I will discuss these applications and opportunities for future work that will make this integration theory more useful in practice. Algebraic Geometry Seminar 3:00 pm in 243 Altgeld Hall, Tuesday, October 30, 2012  Del Edit Copy Submitted by choi29.  Luke Oeding [email] (University of California, Berkeley)Hyperdeterminants of polynomialsAbstract: Hyperdeterminants were brought into a modern light by Gelʹfand, Kapranov, and Zelevinsky in the 1990's. Inspired by their work, I will answer the question of what happens when you apply a hyperdeterminant to a polynomial (interpreted as a symmetric tensor). The hyperdeterminant of a polynomial factors into several irreducible factors with multiplicities. I identify these factors along with their degrees and their multiplicities, which both have a nice combinatorial interpretation. The analogous decomposition for the μ-discriminant of polynomial is also found. The methods I use to solve this algebraic problem come from geometry of dual varieties, Segre-Veronese varieties, and Chow varieties; as well as representation theory of products of general linear groups. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, October 30, 2012  Del Edit Copy Submitted by lidicky.  József Balogh [email] (UIUC Math)Phase transitions in Ramsey-Turán theoryAbstract: Let$f(n)$be a function and$L$a graph. Denote by$RT(L, f(n))$the infimum of$c$such that an$L$-free graph on$n$vertices with independence number at most$f(n)$could have at most$(c+o(1))n^2$edges. Erdős and Sós asked for the largest function$f(n)$such that$RT(K_5,f(n))=0$. Using the Dependent Random Choice Lemma, we answer this question by proving that$RT(K_5,o\left(\sqrt{n\log n}\right))=0$. It was known that$RT(K_5, c\sqrt{n\log n})=1/4$for$c>1$, hence our result is best possible up to a constant factor. Using the Hypergraph Dependent Random Choice Lemma, we extend our result to other cliques. Additionally, we propose many questions: if variants of the Bollobás-Erdős graph exist to give lower bound on$RT(K_t, f(n))$for various pairs of$t$and$f(n)$. Partially joint work with Ping Hu and Miklos Simonovits. Wednesday, October 31, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Wednesday, October 31, 2012  Del Edit Copy Submitted by mbrannan.  Jian Liang (UIUC Math)Tensor Products of Operator Algebras, Part II Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, October 31, 2012  Del Edit Copy Submitted by laugesen.  Sergiy Merenkov [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Rigidity in complex analysis and its discrete counterpartsAbstract: I will start by recalling several rigidity (uniqueness) phenomena in classical complex analysis, then draw parallels with similar questions for circle packings, and finally discuss analogous statements in quasiconformal geometry of carpets and related sets. Special Topology Seminar 4:00 pm in 145 Altgeld Hall, Wednesday, October 31, 2012  Del Edit Copy Submitted by franklan.  Irakli Patchkoria (Universität Bonn)Rigidity in equivariant stable homotopy theoryAbstract: Let G be a finite abelian group or finite (non-abelian) 2-group. We show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique G-equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all "higher order structure" of the 2-local G-equivariant stable homotopy category such as for example equivariant homotopy types of function G-spaces. The theorem can be seen as an equivariant generalization of Schwede's rigidity theorem at the prime 2. Thursday, November 1, 2012 Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, November 1, 2012  Del Edit Copy Submitted by katz.  Dan Freed (UT Austin Math)Twisted equivariant matterAbstract: Wigner's basic theorem about symmetries of quantum mechanics (which may be interpreted as a theorem in Riemannian geometry) leads in many cases to discrete invariants of quantum systems. In joint work with Greg Moore we formulate in mathematical terms the notion of "topological phase" and apply it to the study of topological insulators in condensed matter physics. Topological phases are then measured by twisted equivariant K-theory. Group Theory Seminar 1:00 pm in Altgeld Hall 347, Thursday, November 1, 2012  Del Edit Copy Submitted by kapovich.  Yael Algom-Kfir (Yale University)Small dilatation automorphisms of the free group and their mapping toriAbstract: We consider elements of Out(F_n) that can be represented by a self map of a graph which has the property that a high enough iterate of the map sends every edge over any other edge of the graph. Furthermore, we assume that positive iterates of the map send edges to immersed paths in the graph. These maps are called irreducible train-track maps. To each such automorphism \phi one can attach a real number \lam >1 called the dilatation of \phi. For every n, the set of real numbers realized as dilatations of elements in Out(F_n) is a discrete set however, letting n vary we can get dilatations arbitrarily close to 1. For a fixed n, the smallest dilatation of an element in Out(F_n) is on the order of 2^{1/n}. We define an element to be P-small if its dilatation is smaller than P^{1/n} (there are infinitely many such automorphisms). We prove that for a given P, there exist finitely many 2-complexes so that the mapping torus of any P-small automorphism is obtained by surgery from one of these 2-complexes. This is a direct analog of a theorem of Farb-Leininger-Margalit in the case of Mod(S) for a closed surface S. We also show that the fundamental group of such a mapping torus has a presentation with a uniformly bounded number of generators and relations. This is joint work with Kasra Rafi. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, November 1, 2012  Del Edit Copy Submitted by collier3.  Juan Villeta-Garcia (UIUC Math)Beginner Intersection Theory in Algebraic GeometryAbstract: Given two varieties V and W in \mathbb{P}^n, understanding their intersection V\cap W has been a subject of constant research for most of the 20th century. Many definitions of what an intersection product should be have been given, and subsequently refined. We will give a gentle introduction from the algebraic approach, but also incorporate such constructions as Chern classes and Chow Rings, if time permits. We will have lots of examples! Applied Mathematics Seminar 3:00 pm in 241 Altgeld Hall, Thursday, November 1, 2012  Del Edit Copy Submitted by zrapti.  Richard Kollar (Comenius University, Math)The Krein signature, Evans-Krein function and Hamiltonian-HopfAbstract: We present a couple of applications of a simple graphical interpretation of the Krein signature well-known in the spectral theory of polynomial operator pencils. First, we show a simple generalization of the Evans function, the Evans-Krein function, that allows the calculation of Krein signatures in a way that is easy to incorporate into existing Evans function evaluation codes at virtually no additional computational cost. The graphical Krein signature also enables us to give elegant proofs of index theorems for linearized Hamiltonians in the finite dimensional setting: a general result implying as a corollary Vakhitov-Kolokolov criterion (or Grillakis-Shatah-Strauss criterion) generalized to problems with arbitrary kernels, and a count of real eigenvalues for linearized Hamiltonian systems in canonical form. Finally we demonstrate how the graphical approach can be used to derive new types of criteria prohibiting Hamiltonian-Hopf bifurcations under collisions of two eigenvalues of opposite signature. This is a joint work with Peter Miller (U Michigan). Groupoids and Stacks 3:00 pm in 345 Altgeld Hall, Thursday, November 1, 2012  Del Edit Copy Submitted by lerman.  Eugene Lerman (UIUC Math)Orbifolds as groupoids, 2Abstract: If orbifolds are groupoids, what are the maps? We introduce bibundles. Bibundles with global sections are smooth functors, but in general global sections need not exist. Mathematics Colloquium 4:00 pm in 245 Altgeld Hall, Thursday, November 1, 2012  Del Edit Copy Submitted by kapovich.  Dan Freed (University of Texas - Austin)Chern-Weil forms and abstract homotopy theoryAbstract: We begin by asking some innocent sounding questions in differential geometry. They relate to a standard construction of Chern and Weil. But we give a modern formulation which leads us to abstract homotopy theory and a new take on equivariant de Rham theory. The talk should be accessible to graduate students. Friday, November 2, 2012 Model Theory and Descriptive Set Theory Seminar 3:00 pm in 347 Altgeld Hall, Friday, November 2, 2012  Del Edit Copy Submitted by phierony.  Slawomir Solecki (UIUC Math)Unitary representations of oligomorphic groupsAbstract: We will discuss the paper "Unitary representations of oligomorphic groups" by T. Tsankov (GAFA, (2) 22 (2012), 528-555). This will be the sixth talk of a series about this paper. Monday, November 5, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Monday, November 5, 2012  Del Edit Copy Submitted by mbrannan.  Jian Liang (UIUC Math)Tensor Products of Operator Algebras, Part III Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, November 5, 2012  Del Edit Copy Submitted by fcellaro.  Van Cyr (Northwestern)Nonexpansive$\mathbb Z^2$subdynamics and Nivat’s conjectureAbstract: For a finite alphabet$A$and$\eta: \mathbb Z\to A$, the Morse-Hedlund Theorem states that$\eta$is periodic if and only if there exists$n\in\mathbb N$such that the block complexity function$P_\eta(n)$satisfies$P_\eta(n)\leq n$. In dimension two, a conjecture of M. Nivat states that if there exist$n, k\in\mathbb N$such that the$n\times k$rectangular complexity function,$P_\eta (n, k)$, satisfies$P_\eta(n, k)\leq nk$, then$\eta$is periodic. There have been a number of attempts to prove Nivat’s conjecture over the past 15 years, but the problem has proven difficult. In this talk I will discuss recent joint work with B. Kra in which we associate a$\mathbb Z^2$-dynamical system with$\eta$and show that if there exist$n,k\in\mathbb N$such that$P_\eta(n,k)\leq nk$, then the periodicity of$\eta$is equivalent to a statement about the expansive subspaces of this action. The main result is a weak form of Nivat’s conjecture: if there exist$n, k\in\mathbb N$such that$P_\eta(n,k)\leq \frac{1}{2}nk$, then$\eta$is periodic. Tuesday, November 6, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, November 6, 2012  Del Edit Copy Submitted by franklan.  Jim Davis (Indiana University)Every finite group acts freely and homologically trivially on a product of spheresAbstract: I show that if K is a finite CW complex with finite fundamental group G and universal cover homotopy equivalent to$X=S^{n_1} \times \ldots \times S^{n_k}$, then for every$n \geq dim X$, G acts freely on$X \times S^n$, with the action on homology given by$g \otimes 1 \colon H_*(X) \otimes H_*(S^n) \to H_*(X) \otimes H_*(S^n)$. Recently Unlu and Yalcin constructed for any finite group G, a finite CW complex K with universal cover homotopy equivalent to a product of spheres, where G acts trivially on the homology of the universal cover of K. As a corollary we get the title of the talk. Logic Seminar 1:00 pm in 345 Altgeld Hall, Tuesday, November 6, 2012  Del Edit Copy Submitted by phierony.  Philipp Hieronymi (UIUC Math)Dimension coincidence for expansions of the real fieldAbstract: I will report on joint work with Chris Miller on the question when in expansions of the real field Minkowski dimension and Euclidean dimension coincide. Differential Geometry Seminar 1:00 pm in 243 Altgeld Hall, Tuesday, November 6, 2012  Del Edit Copy Submitted by clein.  Chih-Chung Liu (UIUC Math)The Analysis of Vortex EquationsAbstract: I will introduce the notion of vortices, pairs of connections and smooth sections solving a set of PDE's on a vector bundle called vortex equations. These equations characterize the minimum of certain gauge invariant functionals known as the Yang-Mills Higgs functional. A natural variation of the study of classical vortex equations is to introduce a parameter$s$and let$s \to \infty$, a process known as the "adiabatic limit". I will present the results on the controls of the vortices in suitable Sobelev norms over$s$and the limiting behaviors. The results provide an application on the dynamics of vortices given by the "kinetic energy" of vortices, or a certain "$L^2$metric. As$s \to \infty$, we show that this metric degenerates to a familiar$L^2$metric on the space of holomorphic maps to projective space. The results are joint work with Steven Bradlow and Gabriele La Nave. Probability Seminar 2:00 pm in Altgeld Hall 347, Tuesday, November 6, 2012  Del Edit Copy Submitted by kkirkpat.  Milton Jara [email] (IMPA)Limit theorems for one-dimensional, conservative, weakly assymetric stochastic systemsAbstract: We explain how to obtain the scaling limit of various quantities of interest for one-dimensional, conservative, weakly asymmetric stochastic systems. In particular, we explain the connection between these limits and the celebrated KPZ equation. Algebraic Geometry Seminar 3:00 pm in Altgeld Hall, Tuesday, November 6, 2012  Del Edit Copy Submitted by choi29.  Izzet Coskun (UIC)The birational geometry of the Hilbert scheme of points on surfaces and Bridgeland stabilityAbstract: In this talk, I will discuss the cones of ample and effective divisors on Hilbert schemes of points on surfaces. I will explain a correspondence between the Mori chamber decomposition of the effective cone and the Bridgeland decomposition of the stability manifold. This is joint work with Daniele Arcara, Aaron Bertram and Jack Huizenga. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, November 6, 2012  Del Edit Copy Submitted by lidicky.  Theodore Molla [email] (Arizona State University)Extending the Hajnal-Szemerédi Theorem to directed graphsAbstract: In 1963 Corrádi and Hajnal proved that if$G$is a graph on$3k$vertices with$\delta(G) \ge 2k$then$G$has a$K_3$factor, that is,$k$vertex disjoint copies of the$3$vertex clique. An equivalent form of the Hajnal-Szemerédi Theorem states that if$G$is a graph on$sk$vertices and$\delta(G) \ge (s-1)k$then$G$has a$K_s$factor. We will explore extensions of these results to directed graphs. For a directed graph$D$, let$\delta_{t}(D):= \min_{v \in V(D)}\{ d^+(v) + d^-(v) \}$where$d^+(v)$and$d^-(v)$are the out-degree and in-degree of the vertex$v$respectively and call an oriented$K_s$without directed cycles a transitive$s$-tournament. Analogous to Corrádi and Hajnal's result, we will show that if$D$is a directed graph on$3k$vertices and$\delta_{t}(D) \ge 4k - 1$then$D$contains a transitive$3$-tournament factor. It is then natural to ask if this can be generalized to transitive$s$-tournament factors. We conjecture that if$|D| = sk$and$\delta_{t}(D) \ge 2(s-1)k - 1$then$D$has a transitive$s$-tournament factor. We will discuss a proof of this conjecture for graphs of large order. The proof uses the probabilistic absorbing technique in a manner similar to Levitt, Sárközy and Szemerédi. This is joint work with Andrzej Czygrinow and H.A. Kierstead. Wednesday, November 7, 2012 Operator Algebra Learning Seminar 10:00 am in 147 Altgeld Hall, Wednesday, November 7, 2012  Del Edit Copy Submitted by mbrannan.  Jian Liang (UIUC Math)Tensor Products of Operator Algebras, Part IV IMSE Brown Bag Lunch 12:00 pm in Grainger Engineering Library, Room 335, Wednesday, November 7, 2012  Del Edit Copy Submitted by seminar.  Yuliy Baryshnikov, ECE/Math, and Anil Hirani, CS: Aggregation of preferences and topological social choiceAbstract: This post-election edition will be dedicated to aggregation of preferences and topological social choice. The speakers are Yuliy Baryshnikov, ECE/Math, and Anil Hirani, CS. Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, November 7, 2012  Del Edit Copy Submitted by laugesen.  Kay Kirkpatrick (UIUC Math)A random walk through statistical mechanics: scaling limits and supercool phenomenaAbstract: One of the main goals in statistical mechanics is to derive a macroscopic description of matter from the microscopic interacting particles via scaling limits. I will discuss recent advances on a supercooled phase of matter called Bose-Einstein condensation, in which a gas of quantum particles condenses and behaves like a giant quantum particle. I'll also discuss some challenges for understanding superconductors mathematically, and I'll mention related work in progress. Thursday, November 8, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, November 8, 2012  Del Edit Copy Submitted by ford.  Kevin Ford (UIUC Math)Sets$S$of primes with$p\in S$and$q|(p-1)$implying$q\in S$Abstract: Consider a set$S$of primes such that if$p\in S$and$q|(p-1)$, then$q\in S$. We descibe applications of such sets to Carmichael's conjecture and recent work of the speaker, Konyagin and Luca on groups with Perfect Order Subsets. We also descibe a new bound for the counting function of such sets: either$S$contains all primes or$S$is extremely thin; the number of primes in$S$that are less than$x$is$O(x^{1-c})$for some$c>0$. Group Theory Seminar 1:00 pm in Altgeld Hall 347, Thursday, November 8, 2012  Del Edit Copy Submitted by kapovich.  Paul Schupp (UIUC Math)Multi-pass Automata and Group Word ProblemsAbstract: After reviewing some well-known connections between group theory and formal language theory, I will address a question of Bob Gilman: Is there a reasonable'' class of formal languages which are more general than context-free languages, but much more restricted than linear bounded automata, which tells us something about of group word problems? It seems that the class of multi-pass'' languages is interesting from the point of view. Although starting from automata we will discuss some mapping tori and some flat manifolds. This is joint work with Tullio Ceccerini-Silberstein, Michel Coornaert and Francesa Fiorenzi. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, November 8, 2012  Del Edit Copy Submitted by collier3.  (UIUC Math)Abstract: Cancelled this week. Go to women's seminars instead. Women'sSeminar 2:00 pm in 345 Altgeld Hall, Thursday, November 8, 2012  Del Edit Copy Submitted by funk3.  Mee Seong Im (UIUC Math)Moduli problems through representations of quiversAbstract: Representations of quivers are prominent in many areas of mathematics: in symplectic geometry, representation theory, and mathematical physics to name a few. One interesting fact connecting algebraic geometry and quivers is M Reineke's two page proof that every projective variety is a quiver Grassmannian [arXiv: 1204.5730]. The aim of this talk is for the general audience as I will give a number of examples and use them as a basis as we discuss moduli problems and representations of quivers. I intend to mostly follow King's paper Moduli of Representations of Finite Dimensional Algebras. Minimal mathematical background is linear algebra, and questions are encouraged. Analysis Seminar 2:00 pm in 243 Altgeld Hall, Thursday, November 8, 2012  Del Edit Copy Submitted by aimo.  Alexandra Kolla (UIUC Computer Science)Maximal Inequality for Spherical Means on the HypercubeAbstract: In this talk, we establish a dimension-free ell_2 maximal inequality for spherical means on the Hypercube graph {0,1}^n. We present possible connections to a key open problem in theory of computer science, namely, the Unique Games Conjecture. Combinatorially, this inequality implies the following stronger alternative to the union-bound technique: Assume that we have a binary function f (values 0,1) on the n-dimensional hypercube Hn, with N=2^n vertices. Think of the set X={x\in Hn : f(x)=1} as the set vertices that a malicious adversary "spoils". Assume |X|<\epsilon N, i.e. the adversary can only spoil up to \epsilon fraction of the vertices. Fix a threshold \lambda>\epsilon. Say a (hamming) sphere S(x,r) or radius r around a point x is "bad" if the adversary has spoiled more than \lambda fraction of the points in the shpere. We call a point x "ruined" if *there exists* a radius r for which the sphere S(x,r) around x is bad. Our maximal inequality implies that for every \lambda, there is an absolute constant \epsilon (which does not depend on the dimension n) that if the adversary spoils at most \epsilon fraction of the points then the "ruined" set is a strict subset of the hypercube. Note that applying a union-bound over radii instead, we would not get any useful inequality for the size of the ruined set. Joint work with Aram Harrow (UW) and Leonard Schulman (Caltech). Commutative ring theory seminar 3:00 pm in 243 Altgeld Hall, Thursday, November 8, 2012  Del Edit Copy Submitted by jvalidas.  Youngsu Kim (Purdue University)On the Equality of Ordinary and Symbolic Powers of IdealsAbstract: Symbolic powers of ideals are central objects in commutative algebra and algebraic geometry. For example, in a polynomial ring over an algebraically closed field, the$n$-th symbolic power$P^{(n)}$of a prime ideal P is the set of functions that vanish to order at least$n$along$V(P)$. In this talk, we discuss criteria for the equality of ordinary and symbolic powers. In particular, we are interested to know if the equality of$P^n$and$P^{(n)}$for all$n \leq $a certain bound implies the equality for all$n$(joint work with A. Hosry and J. Validashti). Groupoids and Stacks 3:00 pm in 345 Altgeld Hall, Thursday, November 8, 2012  Del Edit Copy Submitted by lerman.  Eugene Lerman (UIUC Math)Localization of the category of Lie groupoidsAbstract: Why "the obvious" category of Lie groupoids and smooth functors doesn't have enough morphisms and why localization of this category is a bit tricky. Mathematics Colloquium 4:00 pm in 245 Altgeld Hall, Thursday, November 8, 2012  Del Edit Copy Submitted by kapovich.  Marianna Csornyei (University of Chicago)Differentiability of Lipschitz functions and tangents of setsAbstract: We will show how elementary product decompositions of measures can detect directionality in sets, and show how this can be used to describe non-differentiability sets of Lipschitz functions on R^n, and to understand the phenomena that occur because of behaviour of Lipschitz functions around the points of null sets. In order to prove this we will need to prove results about the geometry of sets of small Lebesgue measure: we show that sets of small measure are always contained in a "small" collection of Lipschitz surfaces. The talk is based on a joint work with G. Alberti, P. Jones and D. Preiss. Friday, November 9, 2012 Model Theory and Descriptive Set Theory Seminar 3:00 pm in 347 Altgeld Hall, Friday, November 9, 2012  Del Edit Copy Submitted by phierony.  Aristotelis Panagiotopoulos (UIUC Math)Unitary representations of oligomorphic groupsAbstract: We will discuss the paper "Unitary representations of oligomorphic groups" by T. Tsankov (GAFA, (2) 22 (2012), 528-555). This will be the seventh talk of a series about this paper. Monday, November 12, 2012 Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, November 12, 2012  Del Edit Copy Submitted by fcellaro.  Yiannis Konstantoulas (UIUC)Exponential decay for multiple correlations of$SL(n,\mathbb R)$actions.Abstract: Mozes's theorem implies that a measure preserving, mixing$SL(n,\mathbb R)$action on a probability space$X$is mixing of all orders. In this work we study multiple correlation integrals for$n\geq 3$and prove explicit rates of convergence to the product of the integrals for good spaces of functions on$X$; the results do not depend on Mozes's theorem and thus provide an independent proof of it for$SL(n,\mathbb R)$actions. Tuesday, November 13, 2012 Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, November 13, 2012  Del Edit Copy Submitted by franklan.  Jonathan Campbell (Stanford University)Topological Hochschild homology and Koszul dualityAbstract: Topological Hochschild homology (THH) is an invariant of ring spectra related both to K-theory and topological field theories. In this talk I'll state and prove a theorem concerning the relationship between THH and Koszul duality. I'll introduce the necessary definitions, and in particular say what I mean by "Koszul duality". I will also introduce some$\infty$-categorical background that will be necessary for the proof. Finally, I'll discuss some related results that I believe to be true, and applications of the work above to topological field theories. Number Theory Seminar 11:00 am in 241 Altgeld Hall, Tuesday, November 13, 2012  Del Edit Copy Submitted by ford.  David Zywina (Institute For Advanced Study)Elliptic surfaces and the Inverse Galois ProblemAbstract: The Inverse Galois Problem asks whether every finite group$G$occurs as the Galois group of some extension of$\mathbb{Q}$, i.e., whether there is a Galois extension$K/\mathbb{Q}$such that$Gal(K/\mathbb{Q})$is isomorphic to$G$. This problem is still wide open, even in the special case of simple groups. By studying the Galois action on the \'etale cohomology of some well-chosen elliptic surfaces, we will prove many new cases of the Inverse Galois problem. In particular, we will explain why the simple groups$PSL_2(\mathbb{F}_p)$and$PSp_4(\mathbb{F}_p)$both occur as Galois extensions of$\mathbb{Q}$for all sufficiently large primes$p$. An important role will be played by the Birch and Swinnerton-Dyer conjecture for certain elliptic curves. Logic Seminar 1:00 pm in 345 Altgeld Hall, Tuesday, November 13, 2012  Del Edit Copy Submitted by phierony.  Tobias Kaiser (Universität Passau)A very fi rst step towards an algebraic understanding of the ring of analytic functions that are globally subanalyticAbstract: We are interested in the ring of functions that are analytic and globally subanalytic on a given globally subanalytic domain. The motivation comes from the following two results: The ring of functions that are analytic on a neighbourhood of a compact subanalytic set is Noetherian (see [J. Frisch: Points de platitude d'un morphisme d'espaces analytiques complexes, Inventiones math. 4, 118-138 (1967)]) and the ring of Nash functions (i.e. functions that are analytic and semialgebraic) on a semialgebraic domain is Noetherian (see [J.-J. Risler: Sur l'anneau des fonctions de Nash globales, Ann. Sci. Ecole Norm. Sup. 8, 365-378 (1975)]). To deal with the rings in the subanalytic case it is natural to try rst to understand the local rings given by germs at boundary points of the domain. The most promising tool for that is the rectilinearization theorem proven by Bierstone& Milman and Parusinski. There rings of multivariate Puiseux series comes into the game. We describe these rings as twisted group rings. Harmonic Analysis and Differential Equations 1:00 pm in 347 Altgeld Hall, Tuesday, November 13, 2012  Del Edit Copy Submitted by palbin.  Pierre Albin [email] (UIUC Math)Inverse boundary problems for systems in two dimensionsAbstract: Inverse problems typically consist in trying to recover data about the interior of a domain from observations made at the boundary. For instance, if you know the boundary values of solutions to a Schrodinger equation or a Dirac equation on a surface, can you recover the operators in the interior? I will describe joint work with Colin Guillarmou, Leo Tzou, and Gunther Uhlmann in which we show that, except for an obvious gauge obstruction, the answer is yes. Probability Seminar 2:00 pm in Altgeld Hall 347, Tuesday, November 13, 2012  Del Edit Copy Submitted by kkirkpat.  Wei-Kuo Chen (U Chicago Math)Chaos problem in the mixed even-spin modelsAbstract: The Sherrington-Kirkpatrick (SK) model is one of the most important spin glasses invented by Sherrington and Kirkpatrick with the aim of understanding strange magnetic behaviors of certain alloys. In this talk we will first introduce some well-known results about this model such as the Parisi formula and the limiting behavior of the overlap. Next, we will discuss the problems of chaos in the mixed even-spin models and present mathematically rigorous results including disorder, external field, and temperature chaos. Geometry/Differential Geometry Seminar 2:00 pm in 243 Altgeld Hall, Tuesday, November 13, 2012  Del Edit Copy Submitted by clein.  Andy Sanders (U Maryland)Domains of discontinuity of almost-Fuchsian groupsAbstract: An almost-Fuchsian group is a quasi-Fuchsian group which preserves an embedded minimal disk in hyperbolic 3-space such that the quotient of this disk is a closed minimal surface all of whose principal curvatures lie in the interval (-1, 1). The hyperbolic Gauss map from the minimal disk de fines a di ffeomorphism onto each component of the domain of discontinuity. We will explain how a study of the Gauss map imposes constraints on the structure of the domain of discontinuity. In particular, we will explain how this structure can be used to show that no geometric limit of almost-Fuchsian groups can be doubly degenerate. Algebraic Geometry Seminar 3:00 pm in 243 Altgeld Hall, Tuesday, November 13, 2012  Del Edit Copy Submitted by choi29.  Peng Shan (MIT)Affine Lie algebras and Rational Cherednik Algebras Abstract: Varagnolo-Vasserot conjectured an equivalence between the category O of cyclotomic rational Cherednik algebras and a parabolic category O of affine Lie algebras. I will explain a proof of this conjecture and some applications on the characters of simple modules for cyclotomic rational Cherednik algebras and the Koszulity of its category O. This is a joint work with R. Rouquier, M. Varagnolo and E. Vasserot. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, November 13, 2012  Del Edit Copy Submitted by lidicky.  Paul Horn [email] (Harvard University)Isomorphic subgraphs in graphs and hypergraphsAbstract: We show that any$k$-uniform hypergraph with$n$edges contains two isomorphic edge disjoint subgraphs of size$\tilde{\Omega}(n^{2/(k+1)})$for$k=4,5$and$6$. This is best possible up to a logarithmic factor due to a upper bound construction of Erdős, Pach, and Pyber who show there exist$k$-uniform hypergraphs with$n$edges and with no two edge disjoint isomorphic subgraphs with size larger than$\tilde{O}(n^{2/(k+1)})$. Furthermore, our result extends results Erdős, Pach and Pyber who also established the lower bound for$k=2$(ie. for graphs), and of Gould and Rödl who established the result for$k=3$. In this talk, we'll discuss some of the main ideas of the proof, which is probabilistic, and the obstructions which prevent us from establishing the result for higher values of$k$. We'll also briefly talk about the a connected version of this problem on both graphs and uniform hypergraphs. Mathematics in Science and Society (MSS) 4:00 pm in 245 Altgeld Hall, Tuesday, November 13, 2012  Del Edit Copy Submitted by kapovich.  Mireille Boutin (School of ECE and Dept. of Math, Purdue University)Light-weight Methods for Automatic Recognition in Mobile ApplicationsAbstract: Portable computing devices such as tablets and smart phones are now ubiquitous. For better or for worse, society now expects these devices to replace and even outperform human experts in many domain of applications. In this talk, I will describe some automatic recognition problems which I came across as part of my research on portable device applications, namely the problems of automatically recognizing HAZMAT placards, automatically reading Arabic characters, and interpreting gang graffiti. These problems, I will argue, justify the need for a mathematical theory of shape that is amenable to discrete, noisy data. As a tentative first step towards such a theory, I will define the Pascal Triangle of a discrete gray-scale image as a pyramidal arrangement of complex-valued moments and explore its geometric significance. In particular, we will observe that the entries of row k of this pyramid correspond to the Fourier series coefficients of the order k moment of the Radon transform of the image. Group actions on the plane can be naturally prolonged onto the entries of the Pascal triangle; we will propose simple tests for equivalence and self-equivalence under some common group actions. This is joint work with my graduate students Shanshan Huang and Andrew Haddad. Wednesday, November 14, 2012 Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, November 14, 2012  Del Edit Copy Submitted by laugesen.  Renming Song [email] (UIUC Math)An Introduction to Subordinate Brownian MotionsAbstract: A Levy process is a process with stationary and indpendent increments. Levy processes have been widely used in various fields. However, the class of Levy processes is very large and not very tractable. A subordinate Brownian motion is a Levy process that can be obtained by replacing the time parameter of a Brownian motion by an increasing Levy process (i.e.,subordinator). The subordinator can be thought of as the "operational time" or "intrinsic time". Subordinate Brownian motions form a large sublclass of Levy processes and yet they much more tractable than general Levy processes. In this talk, I will give a brief introduction to subordinate Brownian motions. Thursday, November 15, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, November 15, 2012  Del Edit Copy Submitted by ford.  Jeff Vaaler (Univ. Texas - Austin)Bounds for small generators of number fi eldsAbstract: Let$k$be an algebraic number field with degree$d$over the rational field$\mathbb{Q}$, and discriminant$\Delta_k$. If$k$has a real embedding then we prove that$k$has a generator$\alpha$such that$H(\alpha) \le |\Delta_k|^{1/2d}$, where$H(\alpha)$is the absolute multiplicative Weil height. This verifies a conjecture of W. Ruppert. If$k$has no real embedding the situation is more complicated, and we are only able to obtain a conditional result. In this case we prove a similar bound on the height of a generator for a number fields$k$, but we must assume that the Dedekind zeta-function associated to the Galois closure of$k/\mathbb{Q}$satisfies the generalized Riemann hypothesis. This is joint work with Martin Widmer. Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, November 15, 2012  Del Edit Copy Submitted by katz.  Shinsei Ryu (Ill)Coordinates noncommutativity for three-dimensional topological insulatorsAbstract: We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone of a Chern-Simons invariant in momentum-space. Ref: arXiv:1202.5188 Group Theory Seminar 1:00 pm in Altgeld Hall 347, Thursday, November 15, 2012  Del Edit Copy Submitted by kapovich.  Anton Lukyanenko (UIUC Math)Geodesic coding on the complex hyperbolic modular surfaceAbstract: Continued fractions have been used to study the behavior of geodesics in the modular line$H^2=SL(2; Z)$. Is a similar approach available for other quotients of symmetric spaces? We study the notion of a continued fraction on the Heisenberg group, a step-2 nilpotent group that serves as the boundary of complex hyperbolic plane$CH^2$, and its connection to geodesics in the modular surface$CH^2=SU(2; 1;Z[i])$. Joint work with Joseph Vandehey. Women's Seminar 1:30 pm in Off Site, Thursday, November 15, 2012  Del Edit Copy Submitted by funk3.  Guide: Michelle Delcourt (UIUC Math)CUBE TourAbstract: We will tour the CUBE at the Illinois Simulator Lab (ISL) of the Beckman Institute. The CUBE is an immersive, 3-D visualization chamber, and under the direction of Professor George Francis, we will explore a number of mathematical objects. Francis wrote,"Mathematical visualization is the art of creating a tangible experience with abstract mathematical objects and concepts. While this process has been a cornerstone of the mathematical reasoning process since the times of the ancient geometers, the advent of high-performance interactive computer graphics systems has opened a new era whose ultimate significance can only be imagined." We will meet outside of Coble Hall at 1:30pm. We will take the 1:33pm Silver and get to Vet-Med at 1:42pm. Michelle will lead us from there to the lab. The tour will last until 3:00pm. Analysis Seminar 2:00 pm in 243 Altgeld Hall, Thursday, November 15, 2012  Del Edit Copy Submitted by aimo.  Anne-Katrin Herbig (University of Vienna)Smoothing properties of the Bergman projectionAbstract: Let$D\subset {\mathbb{C}}^n$be a smoothly bounded domain whose Bergman projection$B$maps the Sobolev space$H^{k_1}(D)$continuously to$H^{k_2}(D)$. Then the full Sobolev norm of$Bf$of order$k_2$is controlled by the$L^2-$norm of derivatives of$f$taken along a single, distinguished direction (up to order$k_1$). This work is joint with J. D. McNeal and E. J. Straube. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, November 15, 2012  Del Edit Copy Submitted by collier3.  Brian Collier (UIUC Math)Flat Bundles and Representations of the Fundamental Group.Abstract: Given a manifold$M$and a vector space V, a representation$\rho:\pi_1(M)\rightarrow GL(V)$gives rise to a flat vector bundle via associated bundles and the action of$\pi_1(M)$on the universal cover. Conversely given a vector bundle with a flat structure we get a representation of$\pi_1(M)$. To appreciate this correspondence we will need to discuss some general bundle theory and flat structures this will be done through many examples. This talk should be accessible to all graduate students interested in geometry. Commutative ring theory seminar 3:00 pm in 243 Altgeld Hall, Thursday, November 15, 2012  Del Edit Copy Submitted by jvalidas.  Winfried Bruns [email] (Universitat Osnabruck)Relations of minorsAbstract: We report on joint work with Aldo Conca and Matteo Varbaro. It is a classical theorem that the Grassmannian$G(m,n)$of$m$-subspaces of an$n$-dimensional vector space is defined by the degree$2$Plucker relations. These are obtained as polynomial relations of the Plucker coordinates, which, in their turn, are the$m$-minors ($m\times m$-subdeterminants) of an$m\times n$-matrix$X$of indeterminates, generating the homogeneous coordinate ring of$G(m,n)$. The algebra$A_t$generated by the$t$-minors of$X$for$t\lneq m$is well understood both from the representation-theoretic viewpoint (by work of De Concini-Eisenbud-Procesi) and in its structural properties, as well as the corresponding variety of exterior powers of linear maps (by work of Bruns-Conca). By contrast, the relations of the$t$-minors for$t\lneq m$have not yet been determined, and already in the first non-trivial case relations of degree$3$appear (and for$t \gneq 3$there are non-Plucker relations of degree$2$). We want to describe a representation-theoretic approach that leads to a conjectural description of the relations by which their ideal is generated in degrees$2$and$3$. The conjecture is supported by computational results for small cases. Groupoids and Stacks 3:00 pm in 345 Altgeld Hall, Thursday, November 15, 2012  Del Edit Copy Submitted by lerman.  Eugene Lerman (UIUC Math)A localization of the 2-category of Lie groupoidsAbstract: Embedding the 2 category of Lie groupoids, functors and natural transformation into the bicategory of Lie groupoids, bibundles and isomorphism of bibundles inverts (Morita) equivalences of Lie groupoids. Mathematics Colloquium 4:00 pm in 245 Altgeld Hall, Thursday, November 15, 2012  Del Edit Copy Submitted by kapovich.  Jeff Vaaler (University of Texas - Austin)Diophantine inequalities for height functionsAbstract: This will be a mostly expository talk about recent results and open problems in the theory of height functions. For example, the basic Weil height is defined on$\overline{\mathbf{Q}}^x$, the multiplicative group of nonzero algebraic numbers. We will describe a Banach space that is naturally determined by this height. And we will describe how this Banach space leads to a generalization of the Weil height from elements of$\overline{\mathbf{Q}}^x$to finitely generated subgroups of$\overline{\mathbf{Q}}^x$. The height on subgroups turns out to be equal to the volume of a related convex symmetric subset of a Euclidean space. This height-volume connection leads to a bound on the norm of small integer vectors that provide multiplicative dependencies among finite sets of algebraic numbers. An unusual feature of our approach is that the inequalities we obtain are independent of number fields that contain the initial set of algebraic numbers. Friday, November 16, 2012 Model Theory and Descriptive Set Theory Seminar 3:00 pm in 347 Altgeld Hall, Friday, November 16, 2012  Del Edit Copy Submitted by phierony.  Aristotelis Panagiotopoulos (UIUC Math)Unitary representations of oligomorphic groupsAbstract: We will discuss the paper "Unitary representations of oligomorphic groups" by T. Tsankov (GAFA, (2) 22 (2012), 528-555). This will be the eighth talk of a series about this paper. Monday, November 26, 2012 Algebra, Geometry and Combinatorics 11:00 am in 341 Altgeld Hall, Monday, November 26, 2012  Del Edit Copy Submitted by bwyser.  Jonah Blasiak [email] (University of Michigan)Kronecker coefficients for one hook shapeAbstract: The Kronecker coefficient$g_{\lambda \mu \nu}$is the multiplicity of an irreducible$\mathcal{S}_n$-module$M_\nu$in the tensor product$M_\lambda \otimes M_\mu$. A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. We give such a formula in the case that one of the partitions is a hook shape. Our main tool is Haiman's \emph{mixed insertion}, which is a generalization of Schensted insertion to colored words. Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, November 26, 2012  Del Edit Copy Submitted by fcellaro.  Jayadev Athreya (UIUC)Counting special trajectories for right-angled billiards and pillowcase covers, I.Abstract: In joint work with A. Eskin and A. Zorich, we derive pointwise weak quadratic asymptotics for counting special trajectories for billiards in polygons whose angles are integer multiples of 90 degrees. We describe a proof using ergodic theory on the moduli space of meromorphic quadratic differentials on CP. We will also start to describe how to explicitly compute the constants in our formulas by computing volumes of moduli spaces, which will be continued in our AGC talk on Tuesday. Tuesday, November 27, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Tuesday, November 27, 2012  Del Edit Copy Submitted by ford.  Sun Kim (Ohio State Math)Partitions with parity and part difference conditions, and Bressoud's conjecture.Abstract: George Andrews involved parity restrictions in the Rogers-Ramanujan-Gordon identities to obtain new partition identities, and one of his identities is related to the Gollnitz-Gordon identities. We extend Andrews' partition function, and relate it with the generalized Gollnitz-Gordon identities. Also, we prove partial results of Bressoud's conjecture regrading the generalized Rogers-Ramanujan-Gordon identities. Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, November 27, 2012  Del Edit Copy Submitted by franklan.  Lena Folwaczny (University of Illinois at Chicago)New constructions of virtual knot polynomialsAbstract: Virtual knots and links can be described topologically as embeddings of circles in thickened surfaces (of arbitrary genus) taken up to surface homeomorphisms and 1-handle stabilization. In this talk we give an alternate definition of a virtual knot polynomial, the Affine Index Polynomial, using virtual linking numbers. We call this new definition the Wriggle Polynomial. The Affine Index Polynomial is defined in terms of an integer labeling system of a virtual knot diagram that derives from an essentially unique structure of an affine flat biquandle for flat virtual diagrams, and equality of the definitions is not immediately obvious. Interesting applications of this polynomial to Vassiliev Invariants, Mutant Knots, and the Cosmetic Crossing Change Conjecture are discussed. Harmonic Analysis and Differential Equations 1:00 pm in 347 Altgeld Hall, Tuesday, November 27, 2012  Del Edit Copy Submitted by laugesen.  Dirk Hundertmark [email] (Karlsruhe Institute of Technology)Ludicrous speed of decay of solitons in Hertzian chains Abstract: A Hertzian chain is a model for granular matter. It describes a chain of beads which are just touching each other. The system is modeled by an advance delay equation and the discrete nature of this equation makes is somewhat harder to study than the usual continuum models. It turns out, both experimentally and theoretically, that there are solitary pulses in this system, which are highly localized. The existence of such pulses was also shown rigorously and it was also shown that there are solitary pulses which decay at a double exponential rate, i.e., the asymptotic profile of the pulse goes to zero like exp(-exp(x)). We give an argument that every solitary pulse must decay at this ludicrously fast rate. (Which reminds us of... http://www.youtube.com/watch?v=mk7VWcuVOf0 ) Algebra, Geometry and Combinatorics 2:00 pm in 345 Altgeld Hall, Tuesday, November 27, 2012  Del Edit Copy Submitted by bwyser.  Jayadev Athreya [email] (UIUC Math)Counting special trajectories for right-angled billiards and pillowcase covers, II.Abstract: In joint work with A. Eskin and A. Zorich, we compute volumes of moduli spaces of meromorphic quadratic differentials on CP, via enumerating pillowcase covers. One motivation comes from understanding the (weak) quadratic asymptotics for counting special trajectories for billiards in polygons whose angles are integer multiples of 90 degrees. This talk is a continuation of, but will be independent from, my Ergodic Theory seminar on Monday. In particular, you do not need to have attended the Ergodic Theory talk to understand this talk. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, November 27, 2012  Del Edit Copy Submitted by lidicky.  Alexandr Kostochka [email] (UIUC Math)Hypergraph Ramsey Numbers: Triangles versus CliquesAbstract: It is known that the order of magnitude of the graph Ramsey numbers$R(3,t)$is$t^2/\log t$. We consider an analogue of this problem for uniform hypergraphs. A triangle is a hypergraph consisting of edges$e,f,g$such that$|e \cap f| = |f \cap g| = |g \cap e| = 1$and$e \cap f \cap g = \emptyset$. For all$r \ge 2$, let$R(3,K_t^r)$be the smallest positive integer$n$such that in every red-blue coloring of the edges of the complete$r$-uniform hypergraph$K_n^r$, there exists a red triangle or a blue$K_t^r$. We determine up to a logarithmic factor the order of magnitude of$R(3,K_t^r)$for all$r\ge 3$:$ c_1 (t/\log t)^{3/2} \leq R(3,K_t^r) \leq c_2 t^{3/2}$. When$r=3$, we improve the lower bound to$c_1 t^{3/2}(\log t)^{-3/4}$. This is joint work with D. Mubayi and J. Verstraete. Algebraic Geometry Seminar 3:00 pm in 243 Altgeld Hall, Tuesday, November 27, 2012  Del Edit Copy Submitted by choi29.  Daniel Erman (University of Michigan)Syzygies and Boij--Soederberg TheoryAbstract: For a system of polynomial equations, it has long been known that the relations (or syzygies) among the polynomials provide insight into the properties and invariants of the corresponding projective varieties. Boij--Soederberg Theory offers a powerful perspective on syzygies, and in particular reveals a surprising duality between syzygies and cohomology of vector bundles. I will describe new results on this duality and on the properties of syzygies. This is joint work with David Eisenbud. Analysis area hiring meeting 3:00 pm in 147 Altgeld Hall, Tuesday, November 27, 2012  Del Edit Copy Submitted by aimo.  Abstract: This is the analysis area hiring meeting for assistant and associate professor positions. Mathematics Colloquium: Trjitzinsky Memorial Lectures 4:00 pm in 314 Altgeld Hall, Tuesday, November 27, 2012  Del Edit Copy Submitted by kapovich.  Akshay Venkatesh (Stanford University)Lecture I. The Cohen-Lenstra heuristicsAbstract: The Cohen-Lenstra heuristics predict that class groups of number fields behave like (a certain model of) random abelian group. After explaining what this means (no knowledge of number fields or class groups is assumed) I will briefly discuss a proof of them in the function field setting with Ellenberg and Westerland. The proof is an example of a link between analytic number theory and certain classes of results in algebraic topology ("homological stability"). Please join us for coffee and cookies at 3:30 p.m. in the Common Room (321 Altgeld Hall). A reception will be held in 314 Altgeld immediately following this lecture. Wednesday, November 28, 2012 IMSE Brown Bag Lunch 12:00 pm in Grainger Engineering Library, Room 335, Wednesday, November 28, 2012  Del Edit Copy Submitted by seminar.  Daniel Liberzon (ECE) and Eugene Lerman (Mathematics) Dynamical SystemsAbstract: This meeting of IMSE Seminar deals with dynamical systems. The speakers are Daniel Liberzon, ECE speaking on Almost Lyapunov functions, and Eugene Lerman, Math with a talk on Dynamics on Networks. Mathematics Colloquium: Trjitzinsky Memorial Lectures 4:00 pm in 245 Altgeld Hall, Wednesday, November 28, 2012  Del Edit Copy Submitted by kapovich.  Akshay Venkatesh (Stanford University)Lecture II. The topology of arithmetic manifoldsAbstract: I will discuss the topology of arithmetic hyperbolic 3-manifolds ( but only after explaining what these are!), emphasizing features which seem to differ from the typical behavior of hyperbolic 3-manifolds, and finally how these features seem to be related to deep Diophantine problems like the ABC conjecture. Please join us for coffee and cookies at 3:30 p.m. in the Common Room (321 Altgeld Hall). Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, November 28, 2012  Del Edit Copy Submitted by laugesen.  Abstract: Instead of the usual Math 499 today, we will attend the Trjitzinsky Memorial Lecture. It will help to have attended yesterday's lecture also. Thursday, November 29, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, November 29, 2012  Del Edit Copy Submitted by ford.  Maria Sabitova (CUNY Queens college)On ranks of abelian varieties Math/Theoretical Physics Seminar 12:00 pm in 464 Loomis Laboratory, Thursday, November 29, 2012  Del Edit Copy Submitted by katz.  Tudor Dimofte (IAS School of Natural Sciences)3-Manifolds and 3d Gauge TheoriesAbstract: I will give an overview of a "3d-3d" relation that assigns 3d supersymmetric gauge theories (T[M]) to topological 3-manifolds (M). Physically, the gauge theories come from wrapping M5 branes on M. They can be assembled explicitly and axiomatically using an ideal tetrahedral decomposition of M, together with TQFT-like gluing rules. Various geometric invariants of M (such as SL(N,C) Chern-Simons partition functions) match field-theoretic observables (such as partition functions and indices) of T[M]. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, November 29, 2012  Del Edit Copy Submitted by collier3.  Nerses Aramian (UIUC Math)Milnor's Exotic SphereAbstract: In 1956 Milnor constructed an example of a differentiable manifold that is homeomorphic to$S^7$, but is not diffeomorphic to it. The existence of such an object is quite remarkable, since it shows that not everything about a manifold is determined by its topological structure. In fact, later it was shown that for the case of spheres it is a rare phenomenon to have a unique differentiable structure. I am going to attempt to walk you through the construction of the exotic$S^7$. As the discussion progresses there will be a need to introduce several tools, such as Poincare Duality, Oriented Bordism, Pontrjagin Classes, Hirzebruch Signature Formula. I will attempt to make some of the discussion more homotopical'', so as to convince you that homotopy theory may provide a gateway to generalizations of Milnor's argument. Analysis area hiring meeting 2:00 pm in 243 Altgeld Hall, Thursday, November 29, 2012  Del Edit Copy Submitted by aimo.  Abstract: This is the second analysis area hiring meeting for assistant and associate professor positions, to be held if necessary. Groupoids and Stacks 3:00 pm in 345 Altgeld Hall, Thursday, November 29, 2012  Del Edit Copy Submitted by lerman.  Eugene Lerman (UIUC Math)Why do we need bicategories?Abstract: TBA Mathematics Colloquium: Trjitzinsky Memorial Lectures 4:00 pm in 245 Altgeld Hall, Thursday, November 29, 2012  Del Edit Copy Submitted by kapovich.  Akshay Venkatesh (Stanford University)Lecture III. Langlands program for torsion classesAbstract: In this talk, I'll explain how an extension of the Langlands program links the type of question discussed in lectures I and II, and explain further results on this line. I won't assume any background in the Langlands program -- but a bit of familiarity with modular forms will help. Please join us for coffee and cookies at 3:30 p.m. in the Common Room (321 Altgeld Hall). Monday, December 3, 2012 Ergodic Theory 4:00 pm in 241 Altgeld Hall, Monday, December 3, 2012  Del Edit Copy Submitted by fcellaro.  Slawomir Solecki (UIUC)Closed subgroups generated by generic measure automorphismsAbstract: I will show that for a generic measure preserving transformation$T$, the closed group generated by$T$is a continuous homomorphic image of a closed linear subspace of$L_0(\lambda, {\mathbb R})$, where$\lambda$is Lebesgue measure, and that the closed group generated by$T$contains an increasing sequence of finite dimensional toruses whose union is dense. These results strengthen earlier results by de la Rue, de Sam Lazaro and Ageev, and are related to a conjecture by Glasner and Weiss. I will survey earlier work done on closed subgroups generated by generic measure automorphisms. Operator Algebra 4:00 pm in 147 Altgeld Hall, Monday, December 3, 2012  Del Edit Copy Submitted by liang41.  Ali Kavruk [email] (UIUC Math)Local Lifting Property and ExactnessAbstract: We shall continue on the operator system local lifting property. We exhibit a five dimensional weak expectation property criteria. We finally define exactness in the operator system setting and prove that it is equivalent to (min,el)-nuclearity and nuclear embeddability. Tuesday, December 4, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Tuesday, December 4, 2012  Del Edit Copy Submitted by ford.  David Helm (Univ. Texas at Austin)The integral Bernstein center and the local Langlands correspondence for$GL_n$in familiesAbstract: Understanding the behavior of the local Langlands correspondence as one varies Galois representations in families is an important ingredient in Emerton's recent proof of many cases of the Fontaine-Mazur conjecture. I will explain this question, and its connection to questions involving the Bernstein center, an algebra that acts naturally on a category of smooth representations of$GL_n(F)$, where$F$is a$p$-adic field. Topology Seminar 11:00 am in 243 Altgeld Hall, Tuesday, December 4, 2012  Del Edit Copy Submitted by franklan.  Stephan Stolz (University of Notre Dame)2-dimensional field theories and modular formsAbstract: Graeme Segal suggested two decades ago that the generalized cohomology theory now known as "Topological Modular Form Theory" of a manifold X should be related to families of 2-dimensional field theories parametrized by X. This is an analog of the well-known statement that homotopy classes of families of Fredholm operators parametrized by X can be identified with the K-theory of X. In this talk on joint work with Peter Teichner, I will present a conjectural picture of TMF(X) as concordance classes of families of supersymmetric 2-dimensional Euclidean field theories parametrized by X. Evidence for the conjecture comes from an analogous description of K(X) in terms of 1-dimensional field theories, and our result that the partition function of a supersymmetric 2-dimensional Euclidean field theory is a modular form. The latter is the main focus of the talk. Harmonic Analysis and Differential Equations 1:00 pm in 347 Altgeld Hall, Tuesday, December 4, 2012  Del Edit Copy Submitted by laugesen.  Richard Laugesen [email] (UIUC Math)Sharp Spectral Bounds on Starlike DomainsAbstract: If one knows geometric properties of a domain, such as its area or perimeter, then what inequalities can one deduce on the eigenvalues of the Laplacian for that domain? For example, the fundamental tone (first eigenvalue) and spectral functionals such as the spectral zeta function and heat trace have long been known to be extremal when the domain is a ball, provided the volume of the domain is fixed. We prove complementary bounds in the opposite direction (again sharp for the ball) by introducing an additional geometric quantity that measures the "deviation of the domain from roundness". An intriguing role in the proof is played by volume-preserving diffeomorphisms that are not the identity map. [Joint work with B. Siudeja, U. of Oregon] Differential Geometry 2:00 pm in 243 Altgeld Hall, Tuesday, December 4, 2012  Del Edit Copy Submitted by palbin.  Jesse Gell-Redman (University of Toronto)Harmonic maps of conic surfacesAbstract: Given a diffeomorphism between two compact Riemannian surfaces without boundary and negative curvature, there is a unique map between them that: 1) minimizes the Dirichlet energy, i.e. the$L^2$norm of the derivative, and 2) is homotopic to the original diffeomorphism. This minimizer is a diffeomorphism. These facts are due to Eells-Sampson and Schoen-Yau, and have applications to Teichmueller theory. The same is true for maps between surfaces with conical singularities. We discuss the proof of this result when the cone angles are less than$2\pi$. The linear theory involved is Melrose's b-calculus, and we will give some background and explanation of its use in this context. Algebraic Geometry Seminar 3:00 pm in 243 Altgeld Hall, Tuesday, December 4, 2012  Del Edit Copy Submitted by choi29.  Dawei Chen (Boston College)Extremal effective divisors on the moduli space of curves Abstract: The cone of effective divisors plays a central role regarding the birational geometry of a variety X. In this talk we discuss several approaches that verify the extremality of a divisor, with a focus on the case when X is the moduli space of curves. Graph Theory and Combinatorics 3:00 pm in 241 Altgeld Hall, Tuesday, December 4, 2012  Del Edit Copy Submitted by lidicky.  Ágnes Tóth [email] (Budapest University of Technology and Economics)The asymptotic value of the independence ratio for categorical graph powerAbstract: The independence ratio$i(G)$of a graph$G$is the ratio of the independence number and the number of vertices. The$k$th categorical power of$G$, the graph$G^{\times k}$, is defined on the$k$-length sequences over the vertices of$G$, and two such sequences are connected iff their elements form an edge in$G$at every coordinate. The ultimate categorical independence ratio of a graph$G$is defined by Brown, Nowakowski and Rall as the limit of$i(G^{\times k})$as$k$approaches infinity. Let$a(G)=\max\{\frac{|U|}{|U|+|N_G(U)|}\}$, where the maximum is taken on every independent set$U$of$G$, and$N_G(U)$denotes the neighborhood of$U$in$G$. Alon and Lubetzy proposed the question whether$A(G)=a(G)$if$a(G)\le \frac{1}{2}$, and$A(G)=1$otherwise. In the talk, we will answer this question affirmatively. During the proof we exploit an idea of Zhu that he used on the way when proving the fractional version of Hedetniemi's conjecture. We will also talk about some other open problems related to$A(G)$which are immediately settled by this result. Wednesday, December 5, 2012 Math 499: Introduction to Graduate Mathematics 4:00 pm in 245 Altgeld Hall, Wednesday, December 5, 2012  Del Edit Copy Submitted by laugesen.  Burak Erdogan [email] (UIUC Math)Summability problems in Fourier analysis with applications to geometric measure theory and PDEs Thursday, December 6, 2012 Number Theory Seminar 11:00 am in 241 Altgeld Hall, Thursday, December 6, 2012  Del Edit Copy Submitted by ford.  Shaoshi Chen (North Carolina State Univ. )On the Summability of Bivariate Rational FunctionsAbstract: This talk contains two parts: First, I will give a brief introduction to Zeilberger's method of creative telescoping. Second, I will talk about a recent work, in which we present criteria for deciding whether a bivariate rational function can be written as a sum of two (q)-difference of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated, first, in terms of single sums and, finally, in terms of values of special functions. (This is a joint work with Michael F. Singer) Group Theory Seminar 1:00 pm in Altgeld Hall 347, Thursday, December 6, 2012  Del Edit Copy Submitted by kapovich.  Brian Ray (UIUC Math)General nonexistence of finite strongly relatively rigid sets in Culler-Vogtmann Outer Space.Abstract: Given a subset$\Sigma$of a finitely generated free group, we say that$\Sigma$is (strongly) spectrally rigid if whenever$T, T'$are trees in (the closure of) Culler-Vogtmann Outer Space for which$\| g \|_T = \| g \|_{T'}$for every$g \in \Sigma$, then$T = T'$. Similarly, we say that$\Sigma$is (strongly) relatively rigid at$T$if given a tree$T'$in (the closure of) C-V Outer Space for which$\| g \|_T = \| g \|_{T'}$for every$g \in \Sigma$, then$T = T'$. It is well known that no finite spectrally rigid set exists. Recently, Carette, Francaviglia, Kapovich, and Martino proved that every$T$in C-V Outer Space admits a finite relatively rigid set. We show the existence of a family of trees on the boundary of C-V Outer Space for which no finite strongly relatively rigid set exists. Time permitting, we will discuss how one can promote the result of CFKM and show that every tree in C-V Outer Space admits a finite \emph{strongly} relatively rigid set. Graduate Geometry Topology Seminar 2:00 pm in 241 Altgeld Hall, Thursday, December 6, 2012  Del Edit Copy Submitted by collier3.  Daniel Hockensmith (UIUC Math)An Introduction to JetsAbstract: What is a jet bundle and how does one use it? One expects multiple answers to the latter question, but it is somewhat surprising that there are also multiple answers to the former. We will highlight one approach to jet bundles and apply it to the study of PDE's. In the process, we will discover relationships between geometric objects (i.e. curvature of connections on a fiber bundle) and historically analytic objects (i.e. PDE's and their solutions). Our focus will be placed upon the first jet bundle as there is a plethora of readily visualized examples, but we will certainly talk about jet bundles of arbitrary finite order. Analysis Seminar 2:00 pm in 243 Altgeld Hall, Thursday, December 6, 2012  Del Edit Copy Submitted by aimo.  Koushik Ramachandran (Purdue University)Asymptotic behavior of positive harmonic functions in certain unbounded domainsAbstract: We derive asymptotics of the Martin Kernel at infinity in a large class of unbounded non smooth domains. These include domains whose sections, after rescaling, resemble a Lipschitz cylinder or a Lipschitz cone, e.g., various paraboloids and horns. Applied Mathematics Seminar 3:00 pm in 241 Altgeld Hall, Thursday, December 6, 2012  Del Edit Copy Submitted by zrapti.  Vakhtang Putkaradze (University of Alberta, Math)On violins with rubber strings, or dynamics of elastic rods in perfect friction contact Abstract: One of the most important and challenging problems of elastic rod-based models of polymers is to accurately take into account the self-intersections. Normally, such dynamics is treated with an introduction of a suitable short-range repulsive potential to the elastic string. Inevitably, such models lead to a sliding contact, because of the very nature of the potential interaction between two parts of the string. Such models, however, fail to take into account situations where the small scale structure of the polymer's "surface" is very rough, as is the case with e.g dendronized polymers. Such polymers are more likely to incur the rolling contact dynamics, or at the very least some combination of rolling and sliding contact. It is generally believed to be impossible to model rolling contact, even in the simplest cases, by introducing a contact potential. We derive a consistent motion of two elastic strings in perfect rolling contact, a situation that can be easily visualized by putting two rubber strings in contact. We show that even the contact dynamics is essentially nonlinear, and even if the string's motion away from contact is assumed linear, the contact dynamics leads to strongly nonlinear motion, which we call "contact chaos". We also derive exact motion of contact when the string consists of discrete particles. We finish by presenting some exact solutions of the problem, as well as numerical simulations. Publications: F. Gay-Balmaz, V. Putkaradze, Dynamics of elastic rods in perfect friction contact; Physical Review Letters, to appear (2013) Acknowledgments: Support from Defence Threat Reduction Agency (HDTRA1-10-1-007), NSF-DMS-0908755, the University of Alberta Centennial Fund and WestGrid. Graph Theory and Combinatorics 3:00 pm in 147 Altgeld Hall, Thursday, December 6, 2012  Del Edit Copy Submitted by lidicky.  Dániel Gerbner [email] (Alfréd Rényi Institute of Mathematics)An analogue of the Erdős-Ko-Rado theorem for multisetsAbstract: We are given a finite underlying set$X$. A multiset is an analogue of a subset, but elements can appear more than once. We consider multisets where the sum of the multiplicities is$k$. A family of multisets is called$t$-intersecting if every two members of the family have intersection of size at least$t$. We determine the maximum cardinality of$t$-intersecting families of multisets in case$2k-t \le |X|\$. Joint work with Zoltán Füredi and Máte Vizer.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, December 6, 2012
 Del Edit Copy
Submitted by kapovich.
 Gigliola Staffilani (MIT)Almost Sure Well-posedness for Evolution EquationsAbstract: The center theme of this talk is the effect that randomization on the initial data set has on questions of global well-posedness for a variety of evolution equations. I will start by recalling the notion of Gibbs measure for certain periodic dispersive equations in Hamiltonian form, a work that goes back to Lebowitz-Rose-Speer. I will continue with a short summary of the work of Bourgain, who proved invariance of the Gibbs measure for certain NLS equation and an almost sure global well-posedness as a consequence. I will then continue by illustrating how randomization can be effectively used even when an Hamiltonian structure is not present and as a consequence a Gibbs measure cannot be defined. I will illustrate in this context results proved for example for the Navier-Stokes and wave equations in the supercritical regime.

Friday, December 7, 2012

Model Theory and Descriptive Set Theory Seminar
3:00 pm   in 347 Altgeld Hall,  Friday, December 7, 2012
 Del Edit Copy
Submitted by phierony.
 Slawomir Solecki (UIUC)Idempotents in compact semigroups and Ramsey theoryAbstract: We will discuss the paper 'Idempotents in compact semigroups and Ramsey theory' by H. Furstenberg and Y. Katznelson, Israel J. Math. (3) 68 (1989) 257-270.

Operator Algebra Seminar
4:00 pm   in 147 Altgeld Hall,  Friday, December 7, 2012
 Del Edit Copy
Submitted by liang41.
 Ali Kavruk (UIUC Math)Local Lifting Property and ExactnessAbstract: We continue on low dimensional nuclearity criteria arose from matrix systems which establishes a non-commutative analogue of a classical result of Namioka and Phelps on function systems. We pass to exactness and work on the duality correspondence with the lifting property. If time permits we shall see some equivalent formulations of the Smith-Ward problem on the preservation of essential matricial numerical ranges.

Monday, December 10, 2012

Ergodic Theory
4:00 pm   in 241 Altgeld Hall,  Monday, December 10, 2012
 Del Edit Copy
Submitted by fcellaro.
 Kelly Yancey   [email] (UIUC)On Rigid HomeomorphismsAbstract: We will start by discussing the history of generic results in the setting of measure-preserving automorphisms in ergodic theory. Then we will specifically discuss weakly mixing homeomorphisms that are uniformly rigid and give generic type results for this class of homeomorphisms defined on the two torus and the Klein bottle. We will end with a discussion of spaces which do not admit weakly mixing, uniformly rigid homeomorphisms.

Tuesday, December 11, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, December 11, 2012
 Del Edit Copy
Submitted by franklan.
 John Harper (Purdue University)TQ-homology completion of nilpotent structured ring spectraAbstract: An important theme in current work in homotopy theory is the investigation and exploitation of enriched algebraic structures on spectra that naturally arise, for instance, in algebraic topology, algebraic K-theory, and derived algebraic geometry. Such structured ring spectra or `geometric rings'' are most simply viewed as algebraic-topological generalizations of the notion of ring from algebra and algebraic geometry. This talk will describe recent progress, in joint work with M. Ching, on developing standard tools of the homotopy theory of spaces in this new algebraic-topological context of structured ring spectra, with a special emphasis on recovering algebraic and topological structures from associated homology objects.

Algebra, Geometry and Combinatorics
2:00 pm   in 345 Altgeld Hall,  Tuesday, December 11, 2012
 Del Edit Copy
Submitted by bwyser.
 Daniele Rosso   [email] (University of Chicago)Mirabolic Hecke AlgebrasAbstract: The Hecke Algebra of the symmetric group can be defined as the convolution algebra of GL(V) invariant functions on the variety of pairs of complete flags in a vector space V of dimension d over the finite field with q elements. In the ‘mirabolic’ setting, we consider the variety of triples of two complete flags and a vector in V. The convolution algebra of GL(V) –invariant functions on this variety is very interesting and it was first described by Solomon. For generic q it is a semisimple algebra and its irreducible representations can be parametrized by the partitions of all integers from 0 to d. I will describe some analogues of classical algebraic and combinatorial objects that are found in this new setting. For example, we’ll see Jucys-Murphy elements and their action on Gelfand-Zeitlin bases for irreducible representations. This will give an analogue of the Fock space structure for the category of representations of the Hecke algebra, and lead to a proposed definition of an affine version of the algebra of Solomon (or, equivalently, a mirabolic version of the Affine Hecke algebra). This is work in progress, some of it joint with Jonathan Sun. In addition to discussing some current results, I will point out some directions in which the research is going.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, December 11, 2012
 Del Edit Copy
Submitted by lidicky.
 Jiří Fiala   [email] (Charles University)The k-in-a-path problem for claw-free graphsAbstract: The k-in-a-Path problem is to test whether a graph contains an induced path spanning k given vertices. This problem is NP-complete in general graphs, already when k=3. We show how to solve it in polynomial time on claw-free graphs, when k is an arbitrary fixed integer not part of the input. When k is part of the input, then this problems is NP-complete, even for the class of line graphs, which form a subclass of the class of claw-free graphs. Joint work with Marcin Kaminski, Bernard Lidicky and Daniel Paulusma.

Wednesday, December 12, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in Altgeld Hall,  Wednesday, December 12, 2012
 Del Edit Copy
Submitted by laugesen.
 No meeting this weekAbstract: Good luck with exams!

Thursday, December 13, 2012

Special Presentation: Sandia National Laboratories
9:00 am   in 245 Altgeld Hall,  Thursday, December 13, 2012
 Del Edit Copy
Submitted by seminar.
 (Sandia National Laboratories)Researchers from Sandia National Labs will a present a workshop on their research and discuss opportunities for internships, postdocs, and other collaborationsAbstract: Visit http://www.math.illinois.edu/Bourbaki/sandia-opportunities.html for a detailed schedule of talks.

12:00 pm   in 241 Altgeld Hall,  Thursday, December 13, 2012
 Del Edit Copy
Submitted by collier3.
 Ser-Wei Fu (UIUC Math)Geometry of Quadratic DifferentialsAbstract: Quadratic differentials have an intimidating name. Also the fact that it came from complex analysis has scared off people. I will introduce a very geometric way of describing the space, by semi-translation structures. The talk will be accessible by anyone who knows what a polygon is. The (impossible) goal is to give connections to the fields studied by the GEAR (GEometric structures And Representation varieties) network: Higgs Bundles, Teichmuller Spaces, Dynamics, Represenations, and 3-manifolds.

Illinois Geometry Lab
2:00 pm   in 239 Altgeld Hall,  Thursday, December 13, 2012
 Del Edit Copy
Submitted by lukyane2.
 IGL Scholars (IGL)IGL Open HouseAbstract: Come see IGL scholars display this semester's projects, and hear about our upcoming activities. We will also demonstrate our new 3D printing and scanning technology. All are welcome. Event continues until 4pm.

Tuesday, December 18, 2012

Algebraic Geometry
3:00 pm   in 343 Altgeld Hall,  Tuesday, December 18, 2012
 Del Edit Copy
Submitted by mim2.
 Mee Seong Im (UIUC Math)Invariants and semi-invariants of filtered quiversAbstract: Invariants and semi-invariant polynomials are important in classical invariant theory and in geometric invariant theory (GIT). More precisely, the affine quotient of a variety under the action of a group G is defined by those polynomials invariant under the action of the group while semi-invariant polynomials are used in the construction of GIT quotients. A.D. King in one of his celebrated papers connected the GIT quotient construction and the geometry of quiver variety construction. Quiver varieties are nice and ubiquitous in the sense that they arise in representation theory, mathematical physics, cluster algebras, etc. I will define the notion of a filtered quiver as such examples arise naturally in mathematics. For example, consider a Borel acting on its Lie algebra; how would one strategically produce invariants and semi-invariant polynomials? In another instance, how should one study and manage the B-orbits on the cotangent bundle of the Grothendieck-Springer resolution? Filtered quiver varietes are a generalization of quiver varieties, yet mathematically, they seem to appear as a closed subvariety in an open subset in one of the irreducible components of quivers with relations. I will explain some of my results on how one produces invariants for any acyclic and cyclic filtered quivers. I will then explain how one produces semi-invariants for any acyclic and cyclic filtered quivers. Although there are many interesting examples, I will focus on the B-orbits on Lie(B) and the cotangent bundle of the Grothendieck-Springer resolution. If there is time, I will discuss how filtered quivers are embedded in quivers with relations.

Wednesday, December 19, 2012