Video Lectures

Arithmetic theta series

March 08, 2018

Stephan Kudla

Abstract: In recent joint work with Jan Bruinier, Ben Howard, Michael Rapoport and Tonghai Yang, we proved that a certain generating series for the classes of arithmetic divisors on a regular integral model M of a Shimura variety for a unitary...

video lecture

Admissible heigh pairings of algebraic cycles

March 08, 2018

Shouwu Zhang

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...

video lecture

Special cycles on simple Shimura varieties

March 08, 2018

Wei Zhang

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...

video lecture

Relative character asymptotics and applications

March 06, 2018

Paul Nelson

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....

video lecture

Restriction problem for non-generic representation of Arthur type

March 06, 2018

Wee Teck Gan

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...

video lecture

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

March 06, 2018

Raphaël Beuzart-Plessis

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...

video lecture

About the conjecture of Sakellaridis and Venkatesh on the discrete series for archimedean symmetric spaces

March 06, 2018

Colette Moeglin

video lecture

Boolean function analysis: beyond the Boolean cube (continued).

March 06, 2018

Yuval Filmus

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...

video lecture

Wave-front set of some representations of unipotent reduction of the group SO(2n+1)

March 05, 2018

Jean-Loup Waldspurger

Abstract: Let G be a connected reductive group over a p-adic ﬁeld F and let $\pi$ be an irreducible admissible representation of $G(\overline{F})$. Due to Harish-Chandra, there is a development of the character of $\pi$ near the origin and we can...

video lecture

Supercuspidal L-packets

March 05, 2018

Tasho Kaletha

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...