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for events the day of Tuesday, September 26, 2017.

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Tuesday, September 26, 2017

11:00 am in 241 Altgeld Hall,Tuesday, September 26, 2017

Introduction to Shimura curves

Yifan Yang (National Chiao Tung University)

Abstract: Shimura curves are generalizations of modular curves. The arithmetic aspect of Shimura curves bears a great similarity to that of modular curves. However, because of the lack of cusps on Shimura curves, it is difficult to do explicit computation about them. This makes Shimura curves both interesting and challenging to study. In this talk, we will give a quick introduction to Shimura curves.

12:00 pm in 243 Altgeld Hall,Tuesday, September 26, 2017

Limits of cubic differentials and projective structures

David Dumas (University of Illinois at Chicago)

Abstract: A construction due independently to Labourie and Loftin identifies the moduli space of convex RP^2 structures on a compact surface S with the bundle of holomorphic cubic differentials over the Teichmueller space of S. We study pointed geometric limits of sequences that go to infinity in this moduli space while remaining over a compact set in Teichmueller space. For such a sequence, we construct a local limit polynomial (in one complex variable) which describes the rate and direction of accumulation of zeros of the cubic differentials about the sequence of base points. We then show that this polynomial determines the convex polygon in RP^2 that is the geometric limit of the images of the developing maps of the projective structures. This is joint work with Michael Wolf.

1:00 pm in Altgeld Hall,Tuesday, September 26, 2017

New developments on subelliptic estimates

Martino Fassina (Illinois Math)

Abstract: We first recall some history of subelliptic estimates for d-bar. We then discuss a recent paper of Zaitsev concerning effectiveness of the Kohn algorithm and generalizations by the speaker. The talk should be accessible to graduate students.

1:00 pm in 345 Altgeld Hall,Tuesday, September 26, 2017

Asymptotics of parameterized exponential integrals given by Brownian motion on globally subanalytic sets

Tobias Kaiser (University of Passau)

Abstract: (Joint work with Julia Ruppert.) Understanding integration in the o-minimal setting is an important and difficult task. By the work of Comte, Lion and Rolin, succeeded by the work of Cluckers and Miller, parameterized integrals of globally subanalytic functions are very well analyzed. But very little is known when the exponential function comes into the game. We consider certain parameterized exponential integrals which come from considering the Brownian motion on globally subanalytic sets. We are able to show nice asymptotic expansions of these integrals.

3:00 pm in 241 Altgeld Hall,Tuesday, September 26, 2017

An improved lower bound for Folkman's theorem

József Balogh (Illinois Math)

Abstract: Folkman's Theorem asserts that for each $k \in \mathbb N$, there exists a natural number $n=F(k)$ such that whenever the elements of $[n]$ are two-coloured, there exists a subset $A$ of $[n]$ of size $k$ with the property that all the sums of the form $\sum_{x\in B} x$, where $B$ is a nonempty subset of $A$, are contained in $[n]$ and have the same colour. In 1989, Erdős and Spencer showed that $F(k) \ge 2^{ck^2/\log k}$, where $c>0$ is an absolute constant; here, we improve this bound significantly by showing that $F(k) \ge 2^{2^{k-1}/k}$ for all $k \in \mathbb N$. Joint with Sean Eberhard, Bhargav Narayanan, Andrew Treglown, Adam Zsolt Wagner.

3:00 pm in 243 Altgeld Hall,Tuesday, September 26, 2017

To Be Announced

Mark Penney (University of Oxford / Max Planck Institute (Bonn))