Video Lectures

The work of Green, Tao and Ziegler can be used to prove existence and approximation properties for rational solutions of the Diophantine equations that describe representations of a product of norm forms by a product of linear polynomials. One can...

The P != NP conjecture doesn't tell us what runtime is needed to solve NP-hard problems like 3-SAT and Hamiltonian Path. While some clever algorithms are known, they all require exponential time, and some researchers suspect that this is unavoidable...

There has been substantial progress on algorithmic versions and generalizations of the Lovasz Local Lemma recently, with some of the main ideas getting simplified as well. I will survey some of the main ideas of Moser & Tardos, Pegden, and David...

Let A be an affine variety inside a complex N dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the...