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for events the day of Thursday, April 6, 2017.

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Thursday, April 6, 2017

11:00 am in 241 Altgeld Hall,Thursday, April 6, 2017

Congruences between automorphic forms

Bao V. Le Hung (University of Chicago)

Abstract: The theory of congruences between automorphic forms traces back to Ramanujan, who observed various congruence properties between coefficients of generating functions related to the partition function. Since then, the subject has evolved to become a central piece of contemporary number theory; lying at the heart of spectacular achievements such as the proof of Fermat's Last Theorem and the Sato-Tate conjecture. In my talk I will explain how the modern theory gives satisfactory explanations of some concrete congruence phenomena for modular forms (the $\mathrm{GL}_2$ case), as well as recent progress concerning automorphic forms for higher rank groups. This is joint work with D. Le, B. Levin and S. Morra.

12:00 pm in 243 Altgeld Hall,Thursday, April 6, 2017

Crash course in convex cocompactness.

Autumn Kent (Wisconsin Math)

Abstract: Farb and Mosher introduced the notion of convex cocompactness from Kleinian groups to the theory of mapping class groups, with the beautiful application of potentially producing atoroidal non-hyperbolic groups of finite type, which would provide counterexamples to Gromov's coarse-hyperbolization conjecture for infinite groups. I'll give an overview of the foundations of the theory and the current state of things.

12:30 pm in 464 Loomis Laboratory,Thursday, April 6, 2017


Anatoly Dymarski (Kentucky Physics)

1:00 pm in 7 Illini Hall,Thursday, April 6, 2017

Baire measurable colorings of group actions

Anton Bernshteyn (UIUC Math)

Abstract: Suppose that a countable group $\Gamma$ acts continuously on a Polish space $X$ and denote this action by $\alpha$. Does there exist a Baire measurable coloring $f \colon X \to \mathbb{N}$ satisfying certain local constraints? Or, better to say, can we characterize the coloring problems which admit Baire measurable solutions over $\alpha$? We will show that, on the one hand, there is no such Borel characterization—the problem is complete analytic. On the other hand, when $\alpha$ is the shift action, we prove that, roughly speaking, a Baire measurable coloring exists if and only if it can be found by a greedy algorithm.

2:00 pm in 241 Altgeld Hall,Thursday, April 6, 2017

Primes with restricted digits

Kyle Pratt   [email] (UIUC)

Abstract: Let $a_0 \in \{0,1,2,\ldots,9\}$ be fixed. James Maynard (2016) proved the impressive result that there are infinitely many primes without the digit $a_0$ in their decimal expansions. His theorem is a specific incarnation of a more general problem of finding primes in thin sequences. In this talk I will give a brief discussion about primes in thin sequences. I will also give an overview of some of the tools used in the course of Maynard's proof, including the Hardy-Littlewood circle method, Harman's sieve, and the geometry of numbers.

4:00 pm in 245 Altgeld Hall,Thursday, April 6, 2017

On the transport property of Gaussian measures under Hamiltonian PDE dynamics

Tadahiro Oh (Edinburgh)

Abstract: In probability theory, the transport property of Gaussian measures have attracted wide attention since the seminal work of Cameron and Martin '44. In this talk, we discuss recent development on the study of the transport property of Gaussian measures on spaces of functions under nonlinear Hamiltonian PDE dynamics. As an example, we will discuss the case for the 2-d cubic nonlinear wave equation, for which we introduce a simultaneous renormalization of the energy functional and its time derivative to study the transport property of Gaussian measures on Sobolev spaces. This talk is based on a joint work with Nikolay Tzvetkov (Université de Cergy-Pontoise).