Previous Special Year Seminar

There is a canonical pairing on the Brauer group of a surface over a finite field, which is the analogue of the Cassels-Tate pairing on the Tate-Shafarevich group of a Jacobian variety. An old conjecture of Tate predicts that this pairing is...

An orbit method (or Kirillov method) on compact $p$-adic groups establishes a one-to-one correspondence between irreducible representations and coadjoint orbits of dual blobs. After briefly recalling Howe’s Kirillov theory, we discuss its...

An orbit method (or Kirillov method) on compact $p$-adic groups establishes a one-to-one correspondence between irreducible representations and coadjoint orbits of dual blobs. After briefly recalling Howe’s Kirillov theory, we discuss its...

We will present an introduction to Arthur's trace formula from an analytic point of view. After recalling Arthur's regularization procedure, we will review the absolute convergence and continuity of the trace formula for a large natural class of...

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...

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...

The problem of bounding character twists of low-rank L-functions has been attacked using a variety techniques, including delta methods and analysis of period integral representations. I'll discuss this problem, emphasizing joint work with Roman...