Video Lectures

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...

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...

We give a new local characterization of the Local Langlands Correspondence, using deformation spaces of p-divisible groups, and show its existence by a comparison with the cohomology of some Shimura varieties. This reproves results of Harris-Taylor...

Infinite continuous graphs emerge naturally in the geometric analysis of closed planar sets which cannot be presented as countable union of convex sets. The classification of such graphs leads in turn to properties of large classes of real functions...

The "hard discs" model of matter has been studied intensely in statistical mechanics and theoretical chemistry for decades. From computer simulations it appears that there is a solid--liquid phase transition once the relative area of the discs is...

A perfect matching in a k-uniform hypergraph H = (V, E) on n vertices
is a set of n/k disjoint edges of H, while a fractional perfect matching
in H is a function w : E → [0, 1] such that for each v ∈ V we have
e∋v w(e) = 1. Given n ≥ 3 and 3 ≤ k ≤ n...