# School of Mathematics

## 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

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

## 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.

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

## Supercuspidal L-packets

## 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.

## 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.

## Local eigenvalue statistics of random band matrices

Random band matrices (RBM) are natural intermediate models to study eigenvalue statistics and quantum propagation in disordered systems, since they interpolate between mean-field type Wigner matrices and random Schrodinger operators. In particular, RBM can be used to model the Anderson metal-insulator phase transition (crossover) even in 1d. In this talk we will discuss some recent progress in application of the supersymmetric method (SUSY) and transfer matrix approach to the analysis of local spectral characteristics of some specific types of RBM.

## On the Communication Complexity of Classification Problems

We will discuss a model of distributed learning in the spirit of Yao's communication complexity model. We consider a two-party setting, where each of the players gets a list of labelled examples and they communicate in order to jointly perform a learning task. For example, consider the following problem of Convex Set Disjointness: In this instance Alice and Bob each receive a set of examples in Euclidean space and they need to decide if there exists a hyper-plane that separate the sets.