Video Lectures

Topological spaces given by either (1) complements of coordinate planes in Euclidean space or (2) spaces of non-overlapping hard-disks in a fixed disk have several features in common. The main results, in joint work with many people, give...

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

We develop the droplet scaling theory for the low temperature critical behavior of two-dimensional Ising spin glasses. The models with integer bond energies vs. continuously-distributed bond energies are in the...

To a regular algebraic cuspidal representation of GL(2) over a quadratic imaginary field, whose central character is conjugation invariant, Taylor et al. associated a two dimensional Galois representation which is unramified at l different from p...

Iwasawa developed his theory for class groups in towers of cyclotomic fields partly in analogy with Weil's theory of curves over finite fields. In this talk, we present another such conjectural analogy. It seems intertwined with Leopoldt's...

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...

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...