Video Lectures

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...

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...

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...

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...

Rankin-Selberg integrals provide factorization of certain period integrals into local counterparts. Other, more elusive, periods can be studied in principle by the relative trace formula and other methods.

Following Waldspurger, Ichino-Ikeda...

I will survey what is known about the construction of (the building blocks of) representations of p-adic groups, mention recent developments, and explain some of the concepts underlying all constructions. In particular, I will introduce filtrations...

The hypergraph regularity lemma — the extension of Szemeredi's graph regularity lemma to the setting of k-graphs — is one of the most celebrated combinatorial results obtained in the past decade. By now there are various (very different) proofs of...

Consider a pair $(X,\widehat{L})$ of a regular and projective algebraic variety over $\mathbb{Q}$ and a semipositive adelically metrized line bundle $\widehat{L}$ over $X$. Assume that all of Zhang's successive minima of the pair $(X,\widehat{L})$...

Rankin-Selberg integrals provide factorization of certain period integrals into local counterparts. Other, more elusive, periods can be studied in principle by the relative trace formula and other methods.

Following Waldspurger, Ichino-Ikeda...

In a sequence of extremely fundamental results in the 80's, Kaltofen showed that any factor of n-variate polynomial with degree and arithmetic circuit size poly(n) has an arithmetic circuit of size poly(n). In other words, the complexity class VP is...