## Special cycles on simple Shimura varieties

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

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.

Paul Nelson

ETH Zurich

March 6, 2018

Abstract: Relative (or spherical) characters describe the restriction of a representation to a subgroup. They arise naturally in the study of periods of automorphic forms, e.g., in the setting of conjectures of Gan-Gross-Prasad and Ichino-Ikeda. I will discuss the problem of their asymptotic estimation, emphasizing some known results, open problems and applications.

Wee Teck Gan

National University of Singapore

March 6, 2018

Abstract: The Gross-Prasad conjecture considers a branching problem for generic Arthur packets of classical groups. In this talk, we will describe progress towards extending this conjecture to nongeneric Arthur packets (this is joint work with Gross and Prasad). For GL(n), we describe some recent progress towards this conjecture by Max Gurevich.

Raphael Beuzart-Plessis

CNRS

March 6, 2018

Abstract : Let $E/F$ be a quadratic extension of local fields of characteristic zero. In this talk, I will explain two ways to compute the Plancherel decomposition of $L^2(GL_n(F)\backslash GL_n(E))$. In both cases, the result involves the image of base change from unitary groups to $GL_n(E)$ and is in accordance with a general conjecture of Sakellaridis-Venkatesh on the spectral decomposition of spherical varieties. We will also give applications of our formulas to the so-called Ichino-Ikeda and formal degree conjectures for unitary groups.

Colette Moeglin

IMJ PRG

March 6, 2018

Yuval Filmus

Technion

March 6, 2018

Boolean function analysis traditionally studies Boolean functions on the Boolean cube, using Fourier analysis on the group Z_2^n. Other domains of interest include the biased Boolean cube, other abelian groups, and Gaussian space. In all cases, the focus is on results which are independent of the dimension.

Jean-Loup Waldspurger

Univeristy of Jussieu

March 5, 2018

Tasho Kaletha

University of Michigan

March 5, 2018

Abstract: Harish-Chandra has given a simple and explicit classification of the discrete series representations of reductive groups over the real numbers. We will describe a very similar classification that holds for a large proportion of the supercuspidal representations of reductive groups over non-archimedean local fields (which we may call regular). The analogy runs deeper: there is a remarkable parallel between the characters of regular supercuspidal representations and the characters of discrete series representations of real reductive groups.

Jessica Fintzen

University of Michigan; Member, School of Mathematics

March 5, 2018

Abstract: The building blocks for complex representations of p-adic groups are called supercuspidal representations. I will survey what is known about the construction of supercuspidal representations, mention questions that remain mysterious until today, and explain some recent developments.

Yuval Filmus

Technion

March 5, 2018