Video Lectures

We discuss new results on lozenge tilings on an infinite cylinder, which may be analyzed using the periodic Schur process introduced by Borodin. Under one variant of the q^vol measure, corresponding to random cylindric partitions, the height...

Given a set of integers, we wish to know how many primes there are in the set.  Modern tools allow us to obtain an asymptotic for the number of primes, or at least a lower bound of the expected order, assuming certain strength Type-I information...

Current observations in black-hole astronomy could offer new pathways to constrain deviations from General Relativity. This includes tests of black-hole uniqueness, black-hole stability, and corrections at strong curvature.

• The uniqueness...

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

We recently detected an isolated stellar-mass black hole (BH) unambiguously for the first time, and measured its mass, distance and velocity. We used HST to carry out precise astrometry of the source star of the long-duration, high-magnification...

In this talk I will first review some basics about communication complexity.  Secondly I will survey some (old and new) equivalences between central problems in communication complexity and related questions in additive combinatorics.  In particular...

ECH capacities have found many applications to symplectic embedding problems, most of which in the toric setting. I will discuss a new application of ECH to studying optimal embeddings for non-toric rational surfaces. The key convex geometric...

Projective modules over rings are the algebraic analogs of vector bundles; more precisely, they are direct summands of free modules. Some rings have non-free projective modules. For instance, the ideals of a number ring are projective, and for some...

In this talk, I'll discuss a recent result where we settle the complexities of the maximum-cardinality bipartite matching problem (BMM) up to poly-logarithmic factors in five models of computation:  The two-party communication, AND query, OR query...

It all began with card shuffling. Diaconis and Shahshahani studied the random transpositions shuffle; pick two cards uniformly at random and swap them. They introduced a Fourier analysis technique to prove that it takes 1/2nlogn steps to shuffle a...