Video Lectures

Starting from an example in which the Hitchin correspondence can be written down explicitly, we look at what might be said relating the incidence complex of the boundary of the character variety, and the Hitchin map.

Decoupling inequalities in harmonic analysis permit to bound the Fourier transform of measures carried by hyper surfaces by certain square functions defined using the geometry of the hyper surface. The original motivation has to do with issues in...

At the heart of every local search algorithm is a directed graph on candidate solutions (states) such that every unsatisfactory state has at least one outgoing arc. In stochastic local search the hope is that a random walk will reach a satisfactory...

The pianist Peter Serkin and cellist Fred Sherry are both known for their brilliant renderings of classical repertoire, as well as for their passionate advocacy and electrifying performances of contemporary music. They will present Beethoven's last...

In this lecture, Krause explores the methods used to investigate European population history about the time of agricultural transition. Using genome data, Krause explains how at least three ancestral groups, the Hunter-Gathers, the Early Farmers and...

In this talk, I will present the recent joint work with Yi Zhu on $A^1$-connectedness for quasi-projective varieties. The theory of $A^1$-connectedness for quasi-projective varieties is an analogue of rationally connectedness for projective...

We consider compactifications of the Betti, de Rham and Dolbeault realizations of the character variety. Starting from an example, we look at what can be said, mostly conjecturally, about the relationship between these spaces.

We prove that for any $\epsilon > 0$ it is NP-hard to approximate the non-commutative Grothendieck problem to within a factor $1/2 + \epsilon$, which matches the approximation ratio of the algorithm of Naor, Regev, and Vidick (STOC'13). Our proof...