# School of Mathematics

## Arithmetic theta series

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 group of signature (n-1,1) for an imaginary quadratic field is a modular form of weight n valued in the

first arithmetic Chow group of M. I will discuss how this is proved, highlighting the main steps.

Key ingredients include information about the divisors of Borcherds forms on the integral model

## Euler classes transgressions and Eistenstein cohomology of GL(N)

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

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.

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

## 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

## Restriction problem for non-generic representation of Arthur type

## Relative character asymptotics and applications

## Boolean function analysis: beyond the Boolean cube.

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.

## Representations of p-adic groups

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.