Video Lectures

Computing the volume of a convex body in n-dimensional space is an ancient, basic and difficult problem (#P-hard for explicit polytopes and exponential lower bounds for deterministic algorithms in the oracle model). We present a new algorithm, whose...

What are the possible Hodge numbers of a smooth complex projective variety? We construct enough varieties to show that many of the Hodge numbers can take all possible values satisfying the constraints given by Hodge theory. For example, there are...

I will explain how infinite sequences of flops give rise to some interesting phenomena: first, an infinite set of smooth projective varieties that have equivalent derived categories but are not isomorphic; second, a pseudoeffective divisor for which...

Beauville and Voisin proved that decomposable cycles (intersections of divisors) on a projective K3 surface span a 1-dimensional subspace of the (infinite-dimensional) group of 0-cycles modulo rational equivalence. I will address the following...

Monotone submodular maximization over a matroid (MSMM) is a fundamental optimization problem generalizing Maximum Coverage and MAX-SAT. Maximum Coverage is NP-hard to approximate better than \(1-1/e\), an approximation ratio obtained by the greedy...

My talk will be a broad introduction to what is the (mostly conjectural) higher dimensional generalization of Abel's theorem on divisors on Riemann surfaces, namely, the relationship between the structure of the group of algebraic cycles on a...

In distributed systems, communication between the participants in the computation is usually the most expensive part of the computation. Theoretical models of distributed systems usually reflect this by neglecting the cost of local computation, and...

We consider a Rankin-Selberg integral representation of a cuspidal (not necessarily generic) representation of the exceptional group \(G_2\). Although the integral unfolds with a non-unique model, it turns out to be Eulerian and represents the...