Previous Conferences & Workshops

Erdos conjectured that N points in the plane determine at least c N (log N)^{-1/2} different distances. Building on work of Elekes-Sharir, Nets Katz and I showed that the number of distances is at least c N (log N)^{-1} . (Previous estimates had...

We prove that the Cauchy problem for the Benjamin-Ono-Burgers equation is uniformly globally well-posed in H^1 for all "\epsilon\in [0,1]". Moreover, we show that for any T>0 the solution converges in C([0,T]:H^1) to that of Benjamin-Ono equation as...

THIS LECTURE IS BEING POSTPONED UNTIL NEXT TERM.

Many remarkable questions about prime numbers have natural analogues in the context of elliptic curves. Among them, Artin's primitive root conjecture, the twin prime conjecture, and the Schinzel hypothesis have inspired a broad family of conjectures...

A ``tournament'' is a digraph obtained from a complete graph by directing its edges, and ``colouring'' a tournament means partitioning its vertex set into acyclic subsets (``acyclic'' means the subdigraph induced on the subset has no directed cycles...

Predicting the future for a Hamiltonian dynamical system is an old and notoriously difficult problem. I will present some evidence however that in the simplest situation where one iterates an area preserving map on the 2-disk, solutions to an...

Deift--Simon and Poltoratskii--Remling proved upper bounds on the measure of the absolutely continuous spectrum of Jacobi matrices. Using methods of classical approximation theory, we give a new proof of their results, and generalize them in several...

The correspondence between homotopy types and higher categorical analogs of groupoids which was first conjectured by Alexander Grothendieck naturally leads to a view of mathematics where sets are used to parametrize collections of objects without...

This is a report on some joint work with Mark Reeder and Jiu-Kang Yu. I will review the theory of parahoric subgroups and consider the induced representation of a one-dimensional character of the pro-unipotent radical. A surprising fact is that this...

In this talk, I will explain my joint work with Junecue Suh on when and why the cohomology of Shimura varieties (with nontrivial integral coefficients) has no torsion, based on certain new vanishing theorems we have proved. (All conditions involved...