Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, February 6, 2020.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, February 6, 2020

11:00 am in 241 Altgeld Hall,Thursday, February 6, 2020

#### The Kuznetsov formulas for GL(3)

###### Jack Buttcane (University of Maine)

Abstract: The Kuznetsov formulas for GL(2) connect the study of automorphic forms to the study of exponential sums. They are useful in a wide variety of seemingly unrelated problems in analytic number theory, and I will (briefly) illustrate this with a pair of examples: First, if we consider the roots v of a quadratic polynomial modulo a prime p, then the sequence of fractions v/p is uniformly distributed modulo 1; this is the “mod p equidistribution” theorem of Duke, Friedlander, Iwaniec and Toth. Second, the Random Wave Conjecture states that a sequence of automorphic forms should exhibit features of a random wave as their Laplacian eigenvalues tend to infinity. I will discuss their generalization to GL(3) and applications.

2:00 pm in 347 Altgeld Hall,Thursday, February 6, 2020

#### The Semicircle Law for Wigner Matrices Part 2

###### Kesav Krishnan (UIUC Math)

Abstract: I will introduce Wigner Matrices and their universal properties. I will then state the semi-circle law and sketch out three district proofs, in analogy to the proof of the usual central limit theorem. talk two will discuss the proof based on the method of moments and its relation to enumerative combinatorics.

4:00 pm in 245 Altgeld Hall,Thursday, February 6, 2020

#### Analytic Grothendieck Riemann Roch Theorem

###### Xiang Tang   [email] (Washington University St. Louis)

Abstract: Abstract: In this talk, we will introduce an interesting index problem naturally associated to the Arveson-Douglas conjecture in functional analysis. This index problem is a generalization of the classical Toeplitz index theorem, and connects to many different branches of Mathematics. In particular, it can be viewed as an analytic version of the Grothendieck Riemann Roch theorem. This is joint work with R. Douglas，M. Jabbari, and G. Yu.