Seminar Calendar
for events the week of Monday, October 20, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, October 20, 2014

Symplectic & Poisson Geometry Seminar
3:00 pm   in 341 Altgeld Hall,  Monday, October 20, 2014
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Submitted by jawatts.
 Markus Pflaum (University of Colorado)Inertia spaces and the cyclic homology of convolution algebras over proper Lie groupoidsAbstract: The inertia space of a Lie groupoid encodes interesting topological, geometric, and analytic information about the original Lie groupoid. It is the goal of the talk to explain this point of view using as example the cyclic homology theory of the convolution algebra of a proper Lie groupoid. To this end, the inertia groupoid associated to a proper Lie groupoid is first defined. We show that it is a differentiable stratified groupoid, and non-singular only in exceptional cases. The corresponding quotient space, the inertia space, possesses a Whitney stratification, and is triangulable. Finally, horizontal and basic forms over the inertia space are constructed, and a Hochschild-Kostant-Rosenberg type theorem for the convolution algebra of a proper Lie groupoid is indicated. The talk is based upon joint work, partially in progress, with H. Posthuma and X. Tang, as well as with C. Farsi and Ch. Seaton.

4:00 pm   in 243 Altgeld Hall,  Monday, October 20, 2014
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Submitted by pdnelso2.
 Mychael Sanchez (UIUC Math)Commutative rings in equivariant stable homotopy theoryAbstract: In non-equivariant homotopy theory, E infinity rings play a fundamental role. In the equivariant setting, there are two distinct, but useful notions of an “E infinity" ring spectrum. I’ll discuss both approaches, give examples, and compare them by means of a forgetful functor. This forgetful functor has a left adjoint and a “homotopical” right adjoint. To make sense of this, one needs a suitable equivariant stable category. I’ll motivate such a category by discussing the role that representation spheres play in the equivariant generalizations of classical theorems in stable homotopy theory.

Operator Algebra Learning Seminar
5:15 pm   in Altgeld Hall,  Monday, October 20, 2014
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Submitted by mjunge.
 Ali Kavruk (UIUC)weakly right injective operator systemsAbstract: We study WEP for operator systems.

Tuesday, October 21, 2014

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, October 21, 2014
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Submitted by astraub.
 Atul Dixit   [email] (Tulane University)Zagier polynomials and modified Nörlund polynomialsAbstract: In 1998, Don Zagier studied the numbers $B_{n}^{*}$ which he called 'modified Bernoulli numbers'. They satisfy amusing variants of the properties of the ordinary Bernoulli numbers. Recently, Victor H. Moll, Christophe Vignat and I studied an obvious generalization of the modified Bernoulli numbers, which we call 'Zagier polynomials'. These polynomials are also rich in structure, and a theory parallel to that of ordinary Bernoulli polynomials exists. One thing that was missing was a generalization of Zagier's beautiful exact formula for $B_{2n}^{*}$ for the Zagier polynomials. In an ongoing joint work with M. L. Glasser and K. Mahlburg, we have been able to obtain this generalization which involves Chebyshev polynomials and infinite series of Bessel function $Y_{n}$. I will mainly focus on these results. In the second part of my talk, I will discuss another generalization of the modified Bernoulli numbers that we studied along with A. Kabza, namely 'modified Nörlund polynomials' $B_{n}^{(\alpha)*}$ , $\alpha\in\mathbb{N}$, and obtain their generating function along with applications.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, October 21, 2014
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Submitted by cmalkiew.
 Charles Rezk (UIUC)QX as a Hopf algebraAbstract: The suspension spectrum of the infinite loop space QX admits a product and a coproduct. I'll discuss a theorem of Kuhn, which describes this structure with respect to the Snaith splitting. Then I'll talk about how things simplify after a suitable localization (e.g., with respect to Morava K-theory.)

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, October 21, 2014
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Submitted by berdogan.
 Richard Oberlin (Florida State U. Math)Unit Distance ProblemsAbstract: We consider a continuous version of the Erdos unit distance problem (joint w/ D. Oberlin).

Geometry, Groups and Dynamics/GEAR
1:00 pm   in 243 Altgeld Hall,  Tuesday, October 21, 2014
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Submitted by jathreya.
 Babak Modami (Illinois)Recurrent Weil-Petersson geodesics with non-uniquely ergodic ending laminations.Abstract: A well-known result of H. Masur guarantees that any Teichmuller geodesic which is recurrent to a compact part of the moduli space of Riemann surfaces has a uniquely ergodic vertical foliation. In contrast, we construct recurrent Weil-Petersson geodesics with non-uniquely ergodic ending lamination. This is joint work with Jeffrey Brock. View talk at http://youtu.be/GHczwQwJ3Tg

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, October 21, 2014
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Submitted by kkirkpat.
 Kyle Bradford (University of Nevada, Reno)Adiabatic and Stable Adiabatic TimesAbstract: This talk will detail the stability of Markov chains. One measure of stability of a time-homogeneous Markov chain is a mixing time. I will define similar measures for special types of time-inhomogeneous Markov chains called the adiabatic and stable adiabatic times. I will discuss the use of these Markov chains and I will discuss how the adiabatic and stable adiabatic times relate to mixing times. This talk is an exploration of linear algebra, analysis and probability.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, October 21, 2014
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Submitted by molla.
 Choongbum Lee   [email] (MIT)Grid Ramsey problem and related questionsAbstract: The Hales--Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow. A celebrated theorem of Shelah says that Hales--Jewett numbers are primitive recursive. A key tool used in his proof, now known as the cube lemma, has become famous in its own right. In its simplest form, this lemma says that if we color the edges of the Cartesian product $K_n \times K_n$ in $r$ colors then, for $n$ sufficiently large, there is a rectangle with both pairs of opposite edges receiving the same color. Shelah's proof shows that $n = r^{\binom{r+1}{2}} + 1$ suffices, and more than twenty years ago, Graham, Rothschild and Spencer asked whether this bound can be improved to a polynomial in $r$. We show that this is not possible by providing a superpolynomial lower bound in $r$. We will also discuss a deep connection between this problem and generalized Ramsey numbers, and present a solution to a problem of Erdős and Gyárfás on the transition of asymptotics of generalized Ramsey numbers. Joint work with David Conlon (Oxford), Jacob Fox (MIT), and Benny Sudakov (ETH Zurich)

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 21, 2014
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Submitted by katz.
 Jack Huizenga (UIC Math)Interpolation problems and the birational geometry of moduli spaces of sheavesAbstract: Questions like the Nagata conjecture seek to determine when certain zero-dimensional schemes impose independent conditions on sections of a line bundle on a surface. Understanding analogous questions for vector bundles instead amounts to studying the birational geometry of moduli spaces of sheaves on a surface. We explain how to use higher-rank interpolation problems to compute the cone of effective divisors on any moduli space of sheaves on the plane. This is joint work with Izzet Coskun and Matthew Woolf.

Mathematics in Science and Society (MSS)
4:00 pm   in 245 Altgeld Hall,  Tuesday, October 21, 2014
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Submitted by rdeville.
 David Cai (Courant Institute and Shanghai Jiao Tong University)Mathematical Analysis of Neuronal Network Dynamics in the BrainAbstract: From the perspective of nonlinear dynamical systems, nonequilibrium statistical physics, causal inference, and scientific modeling, we will describe some recent developments of mathematical methods used in analysis of the dynamics of neuronal networks arising from the brain. We will outline some theoretical difficulties in characterization of neuronal network dynamics for the understanding of information processing in the brain.

Actuarial Science & Financial Mathematics
4:00 pm   in 2 Illini,  Tuesday, October 21, 2014
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Submitted by rfeng.
 Xiaochen Jing (UIUC Math)Comonotonic Approximations of Risk Measures for Variable Annuity Guaranteed BenefitsAbstract: The computations of various risk metrics are essential to the quantitative risk management of variable annuity guaranteed benefits. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly to implement. In an attempt to find low-cost solutions, we explore the techniques of comonotonic bounds to produce approximation of risk measures. This is a joint work with Dr. Runhuan Feng.

Wednesday, October 22, 2014

2:00 pm   in 441 Altgeld Hall,  Wednesday, October 22, 2014
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Submitted by fieldst2.
 Bolor Turmunkh (UIUC Math)Introduction to Cluster Algebras and some of their geometric incarnations. Abstract: Cluster Algebras were invented by Fomin and Zelevinsky in order to better understand Lusztig's canonical basis. However, the Cluster Algebra structure turned out to be a rather ubiquitous thing in various areas of Mathematics. They appear in Algebraic Geometry, Integrable Combinatorics, Representation Theory and the theory of Teichmüller spaces to name a few. We will introduce Cluster algebras and state their important properties and results through examples. Finally, we will expose an old friend from Algebraic Geometry to have been a Cluster Algebra all along.

Analysis Seminar
3:00 pm   in 243 Altgeld Hall,  Wednesday, October 22, 2014
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Submitted by laugesen.
 Almut Burchard   [email] (U of Toronto)Geometric stability of the Coulomb energyAbstract: I will discuss new work with Greg Chambers on the Coulomb energy in the context of recent geometric stability results (due to Christ, Figalli, Jerison and others) for functionals that describe non-local interactions. The Coulomb energy of an electrostatic charge distribution is given by the double integral of the Newton potential against the charge density. It is known that the energy of a positive charge distribution increases under symmetrization: The physical reason is that interaction energy between the charges grows as the typical distance between them shrinks. The energy increases strictly, unless the distribution is already radially decreasing about some point. Is this characterization of equality cases "stable"? In other words, must near-maximizers be close to radially decreasing? Greg and I answer this question for charge distributions that are uniform on a set of finite positive volume. Specifically, we bound the difference of a set from a suitably translated ball in terms of the difference in Coulomb energy. Time permitting, I will sketch the proof and mention some open problems.

Integrability and Representation Theory
3:00 pm   in 347 Altgeld Hall,  Wednesday, October 22, 2014
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Submitted by jathreya.
 Aaron Abrams (Washington and Lee)Tiling a square with trianglesAbstract: If you want to cut a square into triangles, what restrictions are there on the areas of the triangles? It turns out that for each combinatorial type of tiling, there's a polynomial relation that must be satisfied by the areas of the triangles in any tiling of the given type. I will describe some new results about this polynomial invariant. (Joint work with J. Pommersheim)

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, October 22, 2014
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Submitted by laugesen.
 Florin Boca (Department of Mathematics, University of Illinois at Urbana-Champaign)Non-commutative toriAbstract: This talk will introduce non-commutative tori (an intensively studied class of C*-algebras), describe some of their main features, and discuss some open problems.

Thursday, October 23, 2014

10:00 am   in 143 Altgeld Hall,  Thursday, October 23, 2014
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Submitted by ackrmnn2.
 Byron Heersink (UIUC Math)Ergodic theory and the distribution of the Farey and Stern-Brocot sequencesAbstract: This talk will first discuss how to lift a cross section of the horocycle flow on SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$) found by Athreya and Cheung to finite covers SL(2,$\mathbb{R}$)/$H$, $H$ a finite index subgroup of SL(2,$\mathbb{Z}$). As an application, we will establish the limiting gap distribution of various subsets of Farey fractions using the ergodic properties of the horocycle flow. We will then discuss the work of Kessebohmer and Stratmann in applying infinite ergodic theory to the distribution of the Stern-Brocot sequence, and give new related results using more elementary methods.

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, October 23, 2014
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Submitted by astraub.
 Kyle Bradford   [email] (University of Nevada)The Erdős-Straus ConjectureAbstract: This talk will outline my recent work on the Erdős-Straus conjecture. Simply put, the Erdős-Straus conjecture states that for every natural number $n$ greater than 1, there exist natural numbers $x$,$y$ and $z$ such that $4/n = 1/x + 1/y + 1/z$. I will give the historical background of the problem and briefly discuss a few partial results before outlining my attempts to prove the conjecture. I will also provide a few conjectures of my own about the problem to open a discussion about possible future work. This problem is very easy to understand, yet very difficult to solve. I would suggest that my talk is accessible to both undergraduate students and advanced researchers alike.

Department of Mathematics Retiree's Luncheon
11:30 am   in Urbana Country Club,  Thursday, October 23, 2014
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Submitted by seminar.

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in Altgeld Hall 243,  Thursday, October 23, 2014
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Submitted by kapovich.
 No seminar today, because of the departmental retirees' luncheon

2:00 pm   in 007 Illini Hall,  Thursday, October 23, 2014
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Submitted by amalik10.
 Atul Dixit (Tulane University Math)Koshliakov transforms and modular-type transformationsAbstract: In 1938, N. S. Koshliakov obtained two remarkable identities which show that the modified Bessel function $K_{\nu}(x)$ is self-reciprocal in two kernels, one of which plays a prominent role in a generalization of the Voronoi summation formula. Motivated by these results, in a joint work with Bruce C. Berndt, Arindam Roy and Alexandru Zaharescu, we consider two integrals transforms which we call the first and second Koshlikov transforms of a function. Using a result from a recent joint work with Victor H. Moll giving conditions for a function to equal its first Koshliakov transform, we obtain a modular-type transformation involving infinite series of a modified Lommel function. Results involving such series are extremely rare. The motivating factor for this result was an incorrect identity on page 336 in Ramanujan's Lost Notebook. We will also show paucity of such results associated with the second Koshliakov transform.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, October 23, 2014
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Submitted by mastroe2.
 Sankar Dutta (UIUC Math)On the Edge Homomorphism of a Spectral SequenceAbstract: The purpose of these talks is to present a connection between the non-vanishing of a specific edge homomorphism of a spectral sequence originating from the associativity property of Hom and Tensor product and several homological conjectures. Ramifications of this observation will be discussed.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, October 23, 2014
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Submitted by seminar.
 Xiuxiong Chen (Stony Brook)CANCELLED

Friday, October 24, 2014

Geometry, Groups and Dynamics/GEAR Seminar
10:00 am   in AH 447,  Friday, October 24, 2014
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Submitted by kapovich.
 Xiuxiong Chen (SUNY Stony Brook)A Liouville theorem on Kaehler Ricci flat metrics in $C^n$ with conical singularities along $\{0\}\times C^{n-1}$Abstract: We prove a new Liouville type theorem which goes back to E. Calabi and Pogorelov. The theorem of Calabi and Pogrelov can be formulated as follows: In $C^n$, any Kaehler Ricci flat metric which depends on $R^n$ (i.e., admitting standard toric symmetry) must be trivial. We prove that, in $C^n$, any Kaehler Ricci flat metric which has conical singularities along $\{0\}\times C^{n-1}$ and is quasi conformal to a standard flat conical metric must be trivial. This has important applications in conical Kaehler geometry (such as regularity for conical Kaehler Einstein metrics). Joint with Yuanqi Wang.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Friday, October 24, 2014
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Submitted by ssolecki.
 Krzysztof Krupinski (University of Wroclaw)Borel cardinalities of bounded invariant equivalence relationsAbstract: Lascar strong types play an important role in model theory. The relation of having the same Lascar strong type is the finest bounded, invariant equivalence relation on a given sort (or product of sorts) of a monster model of a given theory. For a bounded, type-definable equivalence relation, its set of classes equipped with the so-called logic topology forms a compact Hausdorff topological space. However, for relations which are only invariant but not type-definable, the logic topology is not necessarily Hausdorff, so it is not so useful. The question arises how to measure the complexity of the "spaces'' of classes of such relations. One of the ideas is to investigate Borel cardinalities of such relations, which was formalized in my joint paper with A. Pilllay and S. Solecki. During the talk, I will give an overview of the progress which has been made so far in this direction.

Algebra, Geometry and Combinatorics
4:00 pm   in 343 Altgeld Hall,  Friday, October 24, 2014
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Submitted by redavid2.
 Brendan Pawlowski   [email] (University of Minnesota)Cohomology classes of rank varieties and a counterexample to a conjecture of LiuAbstract: Given any diagram (a finite collection of boxes on a grid), one can define an associated symmetric function. In many cases, these symmetric functions contain interesting and nontrivial information related to the diagram: for Young diagrams one obtains Schur functions; for skew diagrams, skew Schur functions; for permutation diagrams, Stanley symmetric functions, which describe reduced words. Liu defined a collection of subvarieties of the Grassmannian indexed by diagrams, and conjectured that their cohomology classes are represented by the corresponding diagram symmetric functions. I will give a counterexample to Liu's conjecture, along with results limiting how badly it can fail in the case of permutation diagrams. I will also discuss a connection to rank varieties (a special case of Knutson-Lam-Speyer's positroid varieties), and some new results on their cohomology classes.