Recently Added

Admissible heigh pairings of algebraic cycles

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.

Special cycles on simple Shimura varieties

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.

Relative character asymptotics and applications

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.

Restriction problem for non-generic representation of Arthur type

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.

The Plancherel formula for L^2(GL_n(F)\GL_n(E)) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups

Raphael Beuzart-Plessis
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.

Supercuspidal L-packets

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.

Representations of p-adic 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.