Video Lectures

An institution dating from antiquity whose formal recognition culminates with the 1951 Geneva Convention on Refugees, asylum has been confronted with a dramatic increase in applicants during the past century. However, this burden has been unevenly...

Resonances are complex analogs of eigenvalues for Laplacians on noncompact manifolds, arising in long time resonance expansions of linear waves. We prove a Weyl type asymptotic formula for the number of resonances in a strip, provided that the set...

We give an arithmetic version of the recent proof of the improved triangle removal lemma by Fox [Fox11], for the group $F_2^n$.
A triangle in $F_2^n$ is a tuple (x,y,z) such that $x+y+z = 0$. The triangle removal lemma for $F_2^n$ states that for...

In the middle of the sixties, A. Lichnerowicz raised the following simple question: “Is the round sphere the only compact Riemannian manifold admitting a noncompact group of conformal transformations?” The talk will present the developments which...

A trusted source of independent and uniform random bits is a basic resource in many computational tasks, such as cryptography, game theoretic protocols, algorithms and physical simulations. Implementing such a source presents an immediate challenge...

This is joint work with A. B. Goncharov. To any convex integer polygon we associate a Poisson variety, which is essentially the moduli space of connections on line bundles on (certain) bipartite graphs on a torus. There is an underlying integrable...

We review the well known microscopic correspondence between random zeros of the Riemann zeta-function and the eigenvalues of random matrices, and discuss evidence that this correspondence
extends to larger mesoscopic collections of zeros or...

Thanks to the work of Katz and Sarnak on L-functions over function fields, we know that the Frobenius classes associated to L-functions of hyperelliptic curves over a finite field with $q$ elements, $F_{q}$, becomes equidistributed in the unitary...