## Period mappings are definable in the o-minimal structure $\mathbb{R}_{an,exp}$

Jacob Tsimerman

University of Toronto

March 13, 2018

Jacob Tsimerman

University of Toronto

March 13, 2018

Paul Nelson

ETH Zurich

March 13, 2018

The problem of bounding character twists of low-rank L-functions has been attacked using a variety techniques, including delta methods and analysis of period integral representations. I'll discuss this problem, emphasizing joint work with Roman Holowinsky in which we give new bounds with simple proofs for the case of GL(3).

Rajiv Gandhi, Dan Zaharopol

Program on Algorithmic and Combinatorial Thinking (PACT), Bridge to Enter Advanced Mathematics (BEAM)

March 12, 2018

We will hear from two passionate creators of successful mentoring programs in math for high school kids in educationally challenged environments. They will give back-to-back talks about their experiences and educational insights.

David Nadler

University of California, Berkeley

March 12, 2018

Ribbon graphs capture the topology of open Riemann surfaces in an elementary combinatorial form. One can hope this is the first step toward a general theory for open symplectic manifolds such as Stein manifolds. We will discuss progress toward such a higher dimensional theory (joint work with Alvarez-Gavela, Eliashberg, and Starkston), and in particular, what kind of topological spaces might generalize graphs. We will also discuss applications to the calculation of symplectic invariants.

Pierre-Henri Chaudouard

IMJ PRG

March 9, 2018

Abstract: The Jacquet-Rallis trace formula is a powerful tool to

study periods of automorphic forms of unitary groups that show

up in Ichino-Ikeda conjecture. In this talk, I will report on the

present state of the Jacquet-Rallis trace formula. Then I will

discuss the problem of the spectral expansion. (joint work with Michal

Zydor).

study periods of automorphic forms of unitary groups that show

up in Ichino-Ikeda conjecture. In this talk, I will report on the

present state of the Jacquet-Rallis trace formula. Then I will

discuss the problem of the spectral expansion. (joint work with Michal

Zydor).

Jacob Tsimerman

University of Toronto

March 9, 2018

Abstract: (joint with N.Mok, J.Pila) Shimura varieties (S) are uniformized by symmetric spaces (H), and the uniformization map Pi:H --> S is quite transcendental. Understanding the interaction of this map with the two algebraic structures is of particular interest in arithmetic, as it is a necessary ingredient for the modern approaches to the Andre-Oort and Zilber-Pink conjectures, as well

Simon Marshall

University of Wisconsin; Member, School of Mathematics

March 9, 2018

Abstract: One of the principles of the endoscopic classification is that if an automorphic representation of a classical group is non-tempered at any place, then it should arise as a transfer from an endoscopic subgroup. One also knows that any representation of a unitary group that contributes to the cohomology of the associated symmetric space outside of middle degree must be non-tempered at infinity. By combining these two ideas, I will derive conjecturally sharp upper bounds for the growth of Betti numbers in congruence towers of complex hyperbolic manifolds.

Peter Sarnak

Professor, School of Mathematics

March 9, 2018

Abstract: A highly excited Maass form on a hyperbolic surface

is expected to behave like a random monochromatic wave .

We will discuss this in connection with the question of the nodal

domains of such forms on arithmetic hyperbolic surfaces with a reflection symmetry .

( Joint work with A.Ghosh and A.Reznikov we will also discuss a recent result of

J.Jang and J.Jung ) .

is expected to behave like a random monochromatic wave .

We will discuss this in connection with the question of the nodal

domains of such forms on arithmetic hyperbolic surfaces with a reflection symmetry .

( Joint work with A.Ghosh and A.Reznikov we will also discuss a recent result of

J.Jang and J.Jung ) .

Wei Zhang

Massachusetts Institute of Technology

March 8, 2018

Abstract: This is a work in progress inspired by the the arithmetic Gan--Gross--Prasad conjecture where one is interested in the arithmetic diagonal cycle on the product of two Shimura varieties. We study special cycles on simple Shimura varieties attached to central

simple algebras with an involution of second kind. We study some local questions arising from the relative trace formula approach.

simple algebras with an involution of second kind. We study some local questions arising from the relative trace formula approach.

Shouwu Zhang

Princeton University

March 8, 2018

Abstract: For a smooth and projective variety X over a global field of dimension n with an adelic polarization, we propose canonical local and global height pairings for two cycles Y, Z of pure dimension p, q satisfying $p+q=n-1$. We will give some explicit arichmedean local pairings by writing down explicit formula for the diagonal green current for some Shimura varieties.