Previous Conferences & Workshops

In a couple of recent works with C. Khare and M. Larsen we contruct finte groups of Lie type B_n, C_n and G_2 as Galois groups over rational numbers. The method combines some established, special cases of the functoriality principle with l-adic...

In 1979, in collaboration with D. Bennequin, we started a direction of research around the study of periodic trajectories of the Reeb vector field $\xi$ on a contact manifold $(M^3, \alpha)$. We will describe in this talk where this direction of...

In this work we study the task of randomness extraction from sources which are distributed uniformly on an unknown algebraic variety. In other words, we are interested in constructing a function (an extractor) whose output is close to uniform even...

The cutoff phenomenon describes a sharp transition in the convergence of a family of ergodic finite Markov chains to equilibrium. Many natural families of chains are believed to exhibit cutoff, and yet establishing this fact is often extremely...

This talk is intended for a general audience. We define and discuss a spectral invariant of closed Riemannian surfaces, namely the zeta regularized trace of inverse of the Laplacian. Physically this corresponds to the sum of squares of the...

Recently, Borgs, Chayes, Lovasz, Sos, Szegedy and Vesztergombi introduced a natural metric on the space of dense graphs, and identified the completion of the metric space that arises. Independently and simultaneously, Janson, Riordan and I defined a...

In this talk, I will at long last give applications of the previous two technical talks. First I will give some direct (and imperfect) applications to representations of the unitary or symplectic groups themselves. Then I will present some...

Harish-Chandra established the Plancherel formula for reductive groups over local fields, in which formal degrees and Plancherel measures are key ingredients. In this talk, we give a natural extension of Langlands' conjecture, which relates...

The main motivation for the theory of mock modular forms comes from the desire to provide a framework in which we can understand the mysterious and intriguing mock theta functions, as well as related functions, like Appell functions and theta...

We address the problem of building a body of specified shape and of specified mass, out of materials of varying density so as to minimize the first Dirichlet eigenvalue. It leads to a free boundary problem and many uniqueness questions, The...