Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, April 29, 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, April 29, 2014

12:00 pm in Lucy Ellis Lounge, 1080 Foreign Languages Building,Tuesday, April 29, 2014

#### Srinivasa Ramanujan: His Life and Notebooks

###### Bruce Berndt (Department of Mathematics, University of Illinois)

1:00 pm in 345 Altgeld Hall,Tuesday, April 29, 2014

#### Decidability problems concerning certain theories of distributive lattices with measure and related weak monadic second order theories of the real order

###### Yevgeniy Gordon (Eastern Illinois)

Abstract: I will discuss some old (early 70-th) results joint with Yu. V. Glebsky concerning theories mentioned in the title. The most part of them was published in Russian in a local journal of the Nizhnij Novgorod State University and was never translated in English. However, they may be of interest in connection with some recent investigations discussed by Ph. Hieronymi in his last talk at the logic seminar.

2:00 pm in Altgeld Hall 347,Tuesday, April 29, 2014

#### On the analysis of stochastic variational inequality problems

###### Uma Ravat (UIUC Math)

Abstract: Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems are complicated by uncertainty. To contend with precisely such a challenge, we consider a stochastic generalization of the variational inequality problem and its extensions in which the components of the mapping contain expectations. When the associated sets are unbounded, ascertaining existence requires having access to analytical forms of the expectations. Naturally, in practical settings, such expressions are often difficult to derive, severely limiting the applicability of such an approach. Consequently, our goal lies in developing techniques that obviate the need for integration. Instead, our emphasis lies in developing sufficiency conditions for claiming existence that are required to hold in an almost-sure sense. We begin by presenting almost-sure sufficiency conditions for stochastic variational inequality problems with single-valued and multi-valued mappings. Next, we extend these statements to quasi-variational regimes. Finally, we refine the obtained results to accommodate stochastic complementarity problems. The applicability of our results is demonstrated on application instances drawn from nonsmooth Nash games and strategic behavior in power markets.

3:00 pm in Altgeld Hall,Tuesday, April 29, 2014

#### Cycles in triangle-free graphs of large chromatic number

###### Alexandr Kostochka   [email] (UIUC Math)

Abstract: Erdos conjectured that a triangle-free graph $G$ of chromatic number $k \geq k_0(\varepsilon)$ contains cycles of at least $k^{2 - \varepsilon}$ different lengths as $k \rightarrow \infty$. We prove the stronger fact that every triangle-free graph $G$ of chromatic number $k \geq k_0(\varepsilon)$ contains cycles of $(\frac{1}{64} - \varepsilon)k^2 \log k$ consecutive lengths, and a cycle of length at least $(\tfrac{1}{4} - \varepsilon)k^2 \log k$. As there exist triangle-free graphs of chromatic number $k$ with at most roughly $4k^2 \log k$ vertices for large $k$, theses results are tight up to a constant factor. We also give new lower bounds on the circumference and the number of different cycle lengths for $k$-chromatic graphs in other monotone classes. This is joint work with B. Sudakov and J. Verstraete.

3:00 pm in 243 Altgeld Hall,Tuesday, April 29, 2014

#### Wall-crossing in genus zero Landau-Ginzburg theory

###### Dustin Ross (University of Michigan)

Abstract: Given a quasi-homogeneous polynomial of degree d, Landau-Ginzburg theory studies certain intersection numbers on the moduli space of d-spin curves (parametrizing curves with d-th roots of the canonical bundle). I will describe a generalization of these intersection numbers obtained by allowing some of the points on the curves to be weighted in the sense of Hassett. As one changes the weights, the invariants thus obtained can be related by a wall-crossing formula. I will explain how the wall-crossing formula generalizes the mirror theorem of Chiodo-Iritani-Ruan, and in particular how it gives a completely enumerative (A-model) interpretation of the mirror phenomenon.

4:00 pm in Altgeld Hall,Tuesday, April 29, 2014

#### The symplectic nature of the fundamental group

###### Brian Collier (UIUC Math)

Abstract: Let $\pi$ be the fundamental group of a RIemann surface and $G$ be a real or complex reductive algebraic group. The goal of this talk is to understand the representation variety $Hom(\pi,G)//G$ from a algebraic geometry perspective. In particular, we will describe the symplectic structure on the representation variety in terms the cup product in group cohomology. The talk will very closely follow the wonderful paper of Bill Goldman with the same title as this talk. All concepts will be explained as if the audience has little or no experience with them, as this is the case for the speaker. Also, the relation of the above topic with HIggs bundles will only be briefly mentioned at the end.

4:00 pm in 314 Altgeld Hall,Tuesday, April 29, 2014

#### A Memorial Service in memory of Heini Halberstam

Abstract: The Department of Mathematics will hold a Memorial Service in memory of Heini Halberstam from 4 to 6 p.m. Tuesday, April 29, 2014. Presentations will be followed by a reception.