Video Lectures

In recent joint work with Alex Arkhipov, we proposed a quantum optics experiment, which would sample from a probability distribution that we believe cannot be sampled (even approximately) by any efficient classical algorithm, unless the polynomial...

A permutation pi=(pi_{1},...,pi_{n}) is consecutive 123-avoiding if there is no sequence of the form pi_i pi_{i+1} pi_{i+2}. More generally, for S a collection of permutations on m+1 elements, this definition extends to define consecutive S...

In this expository talk, I will outline a plausible story of how the study of congruences between modular forms of Serre and Swinnerton-Dyer, which was inspired by Ramanujan's celebrated congruences for his tau-function, led to the formulation of...

The famous theorem of Szemerédi says that for any natural number $k$ and any $a > 0$ there exists n such that if $N >= n$ then any subset $A$ of the set $[N] ={1,2,...,N}$ of size $|A| >= a$ $N$ contains an arithmetic progression of length $k$. We...

Using a version of cylindrical contact homology on the complement of some Reeb orbits in a 3-dimensional contact manifold we will deduce that the existence of closed Reeb orbits with certain topological/dynamical properties implies the existence of...

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

Band matrices are a class of random operators with rows and columns indexed by elements of the d-dimensional lattice, and random entries H(u, v) which are small when the distance between u and v on the lattice is...

Observations of ongoing climate change, paleoclimate data, and climate simulations concur: human-made greenhouse gases have set Earth on a path to climate change with potentially dangerous consequences for humanity. James Hansen, climatologist and...

In a recent paper, DeBacker and Reeder have constructed a piece of the local Langlands correspondence for pure inner forms of unramified p-adic groups and have shown that the corresponding L-packets are stable. In this talk we are going to discuss...

I will describe a joint work with Barnet-Lamb, Gee and Taylor where we establish a potential automorphy result for compatible systems of Galois representations over totally real and CM fields. This is deduced from a potential automorphy result for...