Seminar Calendar
for events the week of Sunday, March 9, 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, March 10, 2014

Mathematics Colloquium - Special Lecture 2013-14
10:00 am   in 243 Altgeld Hall,  Monday, March 10, 2014
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Submitted by seminar.
 Jeremiah Heller (MIT)Galois symmetry and motivic homotopyAbstract: Motivic homotopy theory was introduced by V. Voevodsky as part of his work on the Milnor conjecture. It provides a way of using topological methods as a way to study algebraic varieties over a field. We discuss a new connection between motivic homotopy theory and the study of invariants of manifolds with symmetry. This builds on the classical Galois correspondence and in the case of a real closed field it leads to a surprising generalization of the Fundamental Theorem of Galois theory. This is joint work with K. Ormsby.

Seminar on Applied Topology And Neighboring Areas
2:00 pm   in 147 Altgeld Hall,  Monday, March 10, 2014
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Submitted by hirani.
 Yuriy Mileyko   [email] (Hawaii Math)Duality of Persistence ModulesAbstract: Topological data analysis (TDA), a new approach to handling high-dimensional data, gained a lot of attention lately. TDA focuses on qualitative rather than quantitative information supported by the data. A central concept in TDA is persistent homology, a topological invariant capturing structural changes in continuous objects reflected by the discrete point clouds. In particular, persistent homology allows one to determine the thresholds where new topological features emerge and where they are later destroyed, providing a so-called birth-death decomposition. Birth-death decompositions are often represented as collections of planar points called persistence diagrams, and they have been extensively used in a variety of applications. Often, continuous objects associated with a point cloud are sublevel sets of a function on a manifold. In such a case homological duality results may lead to nice relations between persistence diagrams in different homological dimensions, which doesn't only provide more insight into the theory of persistent homology, but can also be used in practice to reduce computational time. In this talk, I will review some of the existing duality results in persistent homology and show that by focusing not on persistence diagrams but on persistence modules, which are algebraic objects representing birth-death decompositions, one can obtain significantly more general duality results.

Symplectic & Poisson Geometry Seminar
3:00 pm   in 145 Altgeld Hall,  Monday, March 10, 2014
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Submitted by jawatts.
 Roy Wang (Utrecht University Math)Local Rigidity & Nash-Moser MethodsAbstract: J. Conn used analytic methods to prove his theorem on the linearization of Poisson structures. For some time that proof was heuristically interpreted as a local rigidity result for linear, compact, semi-simple Poisson structures. In his thesis I. Marcut made this interpretation rigorous, which lead to surprising new results. In collaboration we aim to isolate the method and formulate a local rigidity theorem, which we apply to other geometrical structures. As an example I sketch a proof of the Newlander-Nirenberg theorem.

Ergodic Theory
4:00 pm   in Altgeld Hall,  Monday, March 10, 2014
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Submitted by jathreya.
 Han Li (Yale)Indefinite Integral Quadratic Forms Beyond Classical Reduction TheoryAbstract: The classical reduction theory of integral quadratic forms was developed by Hermite, Minkowski, Siegel and many others. It is known that a non-degenerate integral quadratic form in n-variables is integrally equivalent to a form whose height (the maximum value of the coefficients) is less than its determinant (up to a multiple constant), and whose value at (1, 0,...0) is less than the n-th root of its determinant. However, for indefinite forms in at least 3 variables it turns out that neither of the estimates is optimal. In this talk we will discuss some classical results and recent effort in improving these estimates. This is a joint work with Prof. Margulis.

Tuesday, March 11, 2014

Harmonic analysis and differential equations
1:00 pm   in 347 Altgeld,  Tuesday, March 11, 2014
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Submitted by vzh.
 Mark Levi   [email] (Penn State Math)Tire tracks, the stationary Schrodinger's equation and forced vibrations.Abstract: I will describe a newly discovered equivalence between the first two objects mentioned in the title. The stationary Schrodinger's equation, a.k.a. Hill’s equation, is ubiquitous in mathematics, physics, engineering and chemistry. Just to mention one application, the main idea of the Paul trap (for which W. Paul earned the 1989 Nobel Prize in physics) amounts to a certain property of Hill's equation. As it turns out, Hill's equation is equivalent to a seemingly completely unrelated problem of “tire tracks”. In addition to this equivalence, I will describe a yet another connection between the tire tracks” problem and the high frequency forced vibrations.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 11, 2014
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Submitted by phierony.
 Philipp Hieronymi (UIUC Math)Expansions of the ordered additive group of real numbers by two discrete subgroupsAbstract: The theory of $(\mathbb{R},<,+,\mathbb{Z},a\mathbb{Z})$ is decidable if $a$ is quadratic. If $a$ is the golden ratio, $(\mathbb{R},<,+,\mathbb{Z},a\mathbb{Z})$ defines multiplication by $a$. The results are established by using the Ostrowski representation of a real number to define the above structures in monadic second order logic of one successor.

Differential Geometry Seminar
1:00 pm   in 243 Altgeld Hall,  Tuesday, March 11, 2014
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Submitted by clein.
 Andy Sanders (UIC Math)A new proof of Bowen's theorem on Hausdorff dimension of quasi-circlesAbstract: A quasi-Fuchsian group is a discrete group of Mobius transformations of the Riemann sphere which is isomorphic to the fundamental group of a compact surface and acts properly on the complement of a Jordan curve: the limit set. In 1979, Bowen proved a remarkable rigidity theorem on the Hausdorff dimension of the limit set of a quasi-Fuchsian group: it is equal to 1 if and only if the limit set is a round circle. This theorem now has many generalizations. We will present a new proof of Bowen's result as a by-product of a new lower bound on the Hausdorff dimension of the limit set of a quasi-Fuchsian group. This lower bound is in terms of the differential geometric data of an immersed, incompressible minimal surface in the quotient manifold. If time permits, generalizations of this result to other convex-co-compact surface groups will be presented.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, March 11, 2014
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Submitted by kkirkpat.
 Rohini Kumar (Wayne State Math)To Be Announced

Descriptive Ergodic Theory Seminar
2:00 pm   in 241 Altgeld Hall,  Tuesday, March 11, 2014
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Submitted by anush.
 Anush Tserunyan (UIUC Math)Generic representations of Abelian groups and extreme amenability (part 3)Abstract: We finish working through the paper "Generic representations of Abelian groups and extreme amenability" by Melleray and Tsankov.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 11, 2014
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Submitted by nevins.
 Jinwon Choi (KIAS)Birational geometry of the moduli space of one-dimensional sheavesAbstract: We study the birational geometry of the moduli space of stable sheaves on $\mathbb{P}^2$ with Hilbert polynomial $dm+1$. We determine the effective/nef cone in terms of natural geometric divisors. We also present the birational model constructed from the locally free resolutions of the general sheaves. The two spaces are related by the Bridgeland-type wall-crossing. As corollaries, we compute the Betti numbers of the moduli spaces when $d \leq 6$. The results confirm the prediction from physics. This is joint work with Kiryong Chung.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 11, 2014
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Submitted by molla.
 Tom Mahoney   [email] (UIUC Math)Characterization of $(2m,m)$-paintable graphs Abstract: A graph $G$ is $(a,b)$-choosable if for any list assignment giving $a$ colors to every vertex admits a coloring assigning each vertex $b$ colors from its list so that the color sets assigned to adjacent vertices are disjoint. Paintability is a generalization of list coloring where list elements are presented in an online fashion. Given $m \ge 1$, a graph $G$ is $(2m,m)$-paintable if and only if it is $2$-paintable. In 2009, Zhu conjectured that $k$-paintable graphs are $(km,m)$-paintable for all $m \ge 1$. Our results prove this conjecture for $k=2$.

Mathematics in Science and Society (MSS)
4:00 pm   in 245 Altgeld Hall,  Tuesday, March 11, 2014
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Submitted by seminar.
 Steven Shreve, Orion Hoch and University Professor (Department of Mathematical Sciences, Carnegie Mellon University)Diffusion Limit of a Limit-Order BookAbstract: With the wholesale movement of the trading of stocks, currencies, and commodities futures to electronic exchanges, the need for models that capture the operation of these exchanges has become paramount. Simple questions such as whether high frequency traders contribute or remove liquidity from the market cannot be studied in the absences of such models. The construction of such models is complicated by their inherent high dimensionality and the strategic play involved. Adapting ideas from queueing theory, we present a simplified model for the limit-order book of an electronic exchange that is driven by Poisson processes. We then describe the limit obtained by diffusion scaling. This is joint work with Christopher Almost and John Lehoczky.

4:00 pm   in 243 Altgeld Hall,  Tuesday, March 11, 2014
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Submitted by villeta2.
 Peter Nelson (UIUC Math)Infinitesimal Algebraic Geometry and Infinitesimal Infinitesimal Algebraic GeometryAbstract: Sometimes the more classical infinitesimal objects attached to a "smooth" group don't contain as much information as one would like, especially in an algebraic setting. I'll discuss one or two (still pretty classical) improvements on the situation. Since I like thinking about universal things, I'll try to say a few things about the moduli spaces of these improvements, and maybe even how they relate to the moduli of the original groups.

Wednesday, March 12, 2014

Decision and Control Lecture Series
3:00 pm   in B02 CSL Auditorium,  Wednesday, March 12, 2014
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Submitted by seminar.
 John Guckenheimer (A. R. Bullis Chair of Mathematics, Cornell University)Complex Oscillations in Multiple Time Scale Dynamical SystemsAbstract: Multiple time scales have a profound impact on dynamical systems. The generic behaviors found in this setting are more complex than those found in systems with a single time scale. This lecture will present examples of biological, engineering and chemical systems that display bursting, chaotic relaxation oscillations and mixed mode oscillations. Recent advances have dramatically improved our understanding of these complex temporal behaviors. A natural classification of different types of bursting and mixed modes is developed and used as a foundation for numerical methods that analyze multiple time scale models.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, March 12, 2014
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Submitted by laugesen.
 Iwan Duursma (Department of Mathematics, University of Illinois at Urbana-Champaign)Applied AlgebraAbstract: We discuss a number of applications in coding theory and cryptography where tools from algebra have been very useful, such as network coding, index coding, distributed storage, secret sharing and multiparty computation.

Thursday, March 13, 2014

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, March 13, 2014
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Submitted by ford.
 Bogdan Petrenko (Eastern Illinois Univ.)Generating an algebra from the probabilistic standpointAbstract: Let A be a ring whose additive group is free abelian of finite rank. The topic of this talk is the following question: what is the probability that several random elements of A generate it as a ring? After making this question precise I will show that it has an interesting answer which can be interpreted as a local-global principle. Some applications will be discussed. This talk will be based on my joint work with with Rostyslav Kravchenko (University of Chicago) and Marcin Mazur (Binghamton University).

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, March 13, 2014
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Submitted by kapovich.
 Spencer Dowdall (UIUC Math)Fibrations and polynomial invariants for free-by-cyclic groupsAbstract: The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial." This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, March 13, 2014
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Submitted by aimo.
 Pekka Pankka (University of Jyväskylä)Beyond virtual nilpotency of fundamental groups of quasireguarly elliptic manifoldsAbstract: By Varopoulos' theorem, the fundamental group of a closed quasiregularly elliptic n-manifold has polynomial order of growth at most n. Thus, by Gromov's theorem, these groups are virtually nilpotent. Having this a priori knowledge, the quasiregular mapping can, however, be used to obtain sharper results on these fundamental groups. I will discuss two recent results: (1) a result with Rami Luisto showing that maximal growth of the group implies the group to be virtually abelian; (2) a result with Enrico Le Donne showing that fundamental groups of closed BLD-elliptic manifolds are (in fact) always virtually abelian. Interestingly, the proofs use completely different geometric methods: the quasiregular result uses Loewner-spaces of Heinonen and Koskela, and the BLD-result Pansu's theorems on Carnot groups.

Special Ergodic Theory Seminar
3:00 pm   in 241 Altgeld Hall,  Thursday, March 13, 2014
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Submitted by jathreya.
 Jacop De Simoi (Toronto)Dynamics of some piecewise smooth Fermi-Ulam modelsAbstract: Fermi-Ulam models are simple one-and-a-half degree of freedom mechanical systems which describe the dynamics of a ball bouncing freely between two oscillating walls. KAM theory implies, if the motion of the walls is sufficiently smooth, existence of invariant tori which prevent any form of diffusion to high energies. In a joint ongoing project with D. Dolgopyat we describe the dynamics of such systems assuming only piecewise smoothness of the wall motions. We are able to give an essentially complete description of the high energy dynamics which turns out to be either hyperbolic (i.e. diffusive) or dominated by elliptic islands. Time permitting I will also explain some work in progress regarding so-called dispersing Fermi-Ulam models and our strategy to attack the problem of ergodicity of this and related models.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, March 13, 2014
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Submitted by seminar.
 Sara Billey (University of Washington)Fingerprint databases for theoremsAbstract: Suppose that M is a mathematician, and that M has just proved theorem T. How is M to know if her result is truly new, or if T (or perhaps some equivalent reformulation of T) already exists in the literature? In general, answering this question is a nontrivial feat, and mistakes sometimes occur. We will discuss several existing databases of theorems which assign a small, language free, searchable "fingerprint" canonically to their theorems. We will also address the question: "How can we canonically fingerprint all theorems and formulas?" which is currently an unsolved problem. Some of the motivation for this discussion came from recent research at the intersection of combinatorics and probability pertaining to peak sets of permutations and statistical processes on graphs called meteors, earthworms and WIMPS. Some of these results will be explained as examples of the main theme. This talk is based on joint work with Chris Burdzy, Soumik Pal, Bruce Sagan, and Bridget Tenner.

Department of Mathematics Social Hour
4:30 pm   in 239 Altgeld Hall,  Thursday, March 13, 2014
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Submitted by seminar.
 Department of Mathematics Social HourAbstract: The Department of Mathematics first social hour gathering will be held from 4:30-6:00 p.m. in the Common Room, 321 Altgeld Hall. Everyone in the department is welcome to attend.

Friday, March 14, 2014