Previous Conferences & Workshops

I will discuss an approach to the subconvexity problem for L-functions based on period integral formulae and amplification. In particular, I will describe work in progress with Ruixiang Zhang that attempts to prove a subconvex bound for the central...

We propose a new second-order method for geodesically convex optimization on the natural hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling problem in time polynomial in the input size and logarithmic in the...

I will talk about some global questions on the concentration properties of automorphic forms that seem to be a natural environment in which to examine the interplay between the geometry and spectrum of spherical varieties, L-functions, and...

Complexity of the geometry, randomness of the potential, and many other irregularities of the system can cause powerful, albeit quite different, manifestations of localization: a phenomenon of confinement of waves, or eigenfunctions, to a small...

We propose a new second-order method for geodesically convex optimization on the natural hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling problem in time polynomial in the input size and logarithmic in the...

In this talk, we construct the so-called Fourier-Jacobi cycles on unitary Shimura varieties. The height pairing of these cycles can be regarded as the arithmetic analogue of classical Fourier-Jacobi periods for the pair of unitary groups of equal...

In addition to offering a formal system for doing ordinary (or "set-level") mathematics, Vladimir Voevodsky’s Univalent Foundations also suggest a new way of studying homotopy theory, called "synthetic homotopy theory".

I will show how synthetic...

A basic but difficult question in the analytic theory of automorphic forms is: given a reductive group G and a representation r of its L-group, how many automorphic representations of bounded analytic conductor are there? In this talk I will present...