Previous Conferences & Workshops

I will survey some characterization results on random walks which stick to a small region unusually long. In application we give a description of unitary matrices of large permanent.

We compare absolute and relative Gromov-Witten invariants with the basic contact vector for very positive divisors. For such divisors, one might expect that these invariants are the same up to a natural multiple. We show that this is indeed the case...

Based on a new decoupling inequality for curves in $\mathbb R^d$, we obtain the essentially optimal form of Vinogradov's mean value theorem in all dimensions (the case $d = 3$ is due to T. Wooley). Various consequences will be mentioned and we will...

Let $G$ be a reductive group over a global field of positive characteristic. In a major breakthrough, Vincent Lafforgue has recently shown how to assign a Langlands parameter to a cuspidal automorphic representation of $G$. The parameter is a...

I will discuss a proof that a complete, non-compact hyperbolic 3- manifold $M$ with finite volume contains an immersed, closed, quasi-Fuchsian surface that separates a given pair of points in the sphere at infinity. Joint with David Futer.

The Langlands program is an intricate network of conjectures, which are meant to connect different areas of mathematics, such as number theory, harmonic analysis and representation theory. One striking consequence of the Langlands program is the...