Video Lectures

Thurston's hyperbolization of fibered 3-manifolds is based on his classification theorem for isotopy classes of surface homeomorphisms. This classification has also been extremely important to the study of dynamical systems on surfaces. The...

Proof complexity studies the complexity of mathematical proofs, with the aim of exhibiting (true) statements whose proofs are always necessarily long. One well-known proof system is Hilbert's Nullstellensatz, which shows that if the family $F=\{f_1...

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.

Edward T. Cone Concert Series Ralph van Raat Amsterdam/New Amsterdam November 14, 2014 For decades now, there has been a close association between the preeminent Dutch composer Louis Andriessen and a significant group of American minimalist and...

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...

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...

One of the major challenges of the research in circuit complexity is proving super-polynomial lower bounds for de-Morgan formulas. Karchmer, Raz, and Wigderson suggested to approach this problem by proving that formula complexity behaves "as...