Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, October 14, 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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Tuesday, October 14, 2014

11:00 am in 243 Altgeld Hall,Tuesday, October 14, 2014

#### Recognizing small model structures

###### Inna Zakharevich   [email] (U Chicago)

Abstract: Model categories have been widely used over the past 40 years, but they rarely arise "in the wild"; instead, one is usually given a category C with a subcategory wC of weak equivalences, and would like to construct a model structure around those. Unfortunately, there is no known algorithm for doing so, and no general recognition principle that says that such a model structure exists. In this talk we will investigate this question in the case where C is small (and thus a preorder). In the end we will give simple necessary and sufficient conditions for a model structure on C with weak equivalences W to exist.

1:00 pm in 345 Altgeld Hall,Tuesday, October 14, 2014

#### The Generic Point Problem and closed subgroups of $S_\infty$

###### Andrew Zucker (Carnegie Mellon University)

Abstract: A topological group $G$ is said to have the Generic Point Property if the universal minimal flow $M(G)$ has a generic point, a point whose orbit is comeager. This in turn implies that any minimal $G$-flow has a generic point. Angel, Kechris, and Lyons asked the following question, known as the Generic Point Problem: If $G$ is a Polish group and the universal minimal flow $M(G)$ is metrizable, does $G$ have the Generic Point Property? In this talk, we will discuss the case where $G$ is a closed subgroup of $S_\infty$; here the answer is affirmative. To show this, we work with an explicit characterization of the greatest $G$-ambit and introduce some new tools in structural Ramsey theory.

1:00 pm in 243 Altgeld Hall,Tuesday, October 14, 2014

#### Polygons, polynomials, fences, and flows

###### David Dumas (UIC)

Abstract: In a recent paper with Michael Wolf, we use affine differential geometry to construct a homeomorphism between the moduli space of polynomial cubic differentials on the complex plane and the space of projective equivalence classes of convex polygons in RP^2. In this talk I will briefly recall the results of this project, and then focus primarily on discussing various connections, questions, and conjectures suggested by this work. These include an interpretation of our main theorem in terms of a family of rank-3 meromorphic Higgs bundles, a conjectural relation with the Stokes phenomenon, and a question about the Poisson geometry of the space of twisted polygons. View talk at http://youtu.be/7ywL7IzHyQw

2:00 pm in Altgeld Hall 347,Tuesday, October 14, 2014

#### Sequential Change Detection for Fractional SDEs

###### Alexandra Chronopoulou (UIUC IESE)

Abstract: We will consider the problem of sequentially detecting a change in a stochastic process that satisfies a fractional stochastic differential equation with an arbitrary Hurst index, H. For this class of dynamics, we will establish sufficient conditions for the Cumulative Sums (CUSUM) test to be an exact (non-asymptotic) solution to Lorden's minimax optimal stopping problem. In this way, we will extend well-known optimality properties of CUSUM for diffusion processes. The main techniques for these extensions come from fractional calculus and Malliavin calculus.

3:00 pm in 241 Altgeld Hall,Tuesday, October 14, 2014

#### Hajnal-Szemerédi type theorems

###### Theodore Molla   [email] (UIUC Math)

Abstract: An equitable $k$-coloring of a graph $G$ is a proper $k$-coloring in which every pair of color classes differ in size by at most one. In 1970 Hajnal and Szemerédi proved that every graph with maximum degree less than $k$ has an equitable $k$-coloring. This theorem is easily seen to be best possible: complete graphs, odd cycles and balanced complete bipartite graphs with odd sized parts are all not equitably $k$-colorable when $k$ is the maximum degree. In 1994 Chen, Lih and Wu conjectured that these are the only connected graphs that are not equitable $k$-coloring and have maximum degree at most $k$. This conjecture is still open, but a few special cases have been proved. In this talk, we will discuss an Ore-type result which implies the Chen-Lih-Wu conjecture for $k$-equitable colorings in graphs with $3k$ vertices as well as other extension and generalizations of the Hajnal-Szemerédi Theorem. This work is joint with H.A. Kierstead, Alexandr Kostochka, and Elyse Yeager.

3:00 pm in 243 Altgeld Hall,Tuesday, October 14, 2014

#### The refined BPS - virtual Poincare polynomial conjecture

###### Sheldon Katz (UIUC Math)

Abstract: My collaborators and I have conjectured that the refined BPS invariants of a Calabi-Yau threefold are equivalent in a precise way to the virtual Poincare polynomials of the moduli space of PT theory. In this talk, I start with background on BPS invariants of Calabi-Yau threefolds and their refinement, along with background on PT theory and its motivic extension. I then formulate the conjecture and provide evidence.

4:00 pm in 314 Altgeld Hall,Tuesday, October 14, 2014

#### Symplectic resolutions and Lie algebras

###### Andrei Okounkov (Columbia Univ)

Abstract: Note the unusual day. Please attend the Trjitzinsky Lecture by Andrei Okounkov (Columbia Univ) at 4 p.m. in 314 Altgeld Hall.
In geometric representation theory, one often links the properties of noncommutative algebras to the geometry of their commutative degenerations, and also often aims to make an algebra act on cohomology or K-theory of another algebraic variety. These points of view are in a certain sense dual, and my goal in these lectures will be to discuss several recent ideas and advances in this direction.

4:00 pm in 314 Altgeld Hall,Tuesday, October 14, 2014

#### Symplectic resolutions and Lie algebras

###### Andrei Okounkov (Columbia University)

Abstract: In geometric representation theory, one often links the properties of noncommutative algebras to the geometry of their commutative degenerations, and also often aims to make an algebra act on cohomology or K-theory of another algebraic variety. These points of view are in a certain sense dual, and my goal in these lectures will be to discuss several recent ideas and advances in this direction.

Andrei Okounkov of Columbia University will deliver the Trjitzinsky Lectures on October 14, 15, 16, 2014. A reception will be held from 5-6 p.m. in 239 Altgeld Hall following the Oct 14 lecture.