Video Lectures

I will discuss joint work with Olga Plamenevskaya studying symplectic fillings of links of certain complex surface singularities, and comparing symplectic fillings with complex smoothings. We develop characterizations of the symplectic fillings...

One of Alan Turing's most influential papers is his 1950 Computing machinery and intelligence, in which he introduces the famous "Turing test" for probing the nature of intelligence by evaluating the abilities of machines to behave as humans. In this...

A group is said to have bounded generation (BG) if it is a finite product of cyclic subgroups. We will survey the known examples of groups with (BG) and their properties. We will then report on a recent result (joint with P. Corvaja, J. Ren and U...

I will report on a project joint with Roman Bezrukavnikov (and partly with Laura Rider) aiming at constructing a variant for positive-characteristic coefficients of the equivalence constructed by Bezrukavnikov in "On two geometric realizations of an...

This is the final talk in a 3-part series whose goal is to give background as well as a self contained proof of Chen's recent breakthrough on the KLS conjecture and slicing problem. After becoming familiar with the construction of stochastic...

Korevaar and Schoen introduced, in a seminal paper in 1993, the notion of `Dirichlet energy’ for a map from a smooth Riemannian manifold to a metric space. They used such concept to extend to metric-valued maps the regularity theory by Eells-Sampson...

Imagine a 1D curve, then use it to fill a 2D manifold that covers an arbitrary 3D object – this computationally intensive materials challenge has been realized in the ancient technology known as knitting. This process for making functional materials...

Up to a finite covering, a sequence of nested subvarieties of an affine algebraic variety just looks like a flag of vector spaces (Noether); understanding this « up to » is a primary motivation for a fine study of finite coverings.

The aim of this...

Khovanov showed, more than 20 years ago, that there is a deeper theory underlying the Jones polynomial. The``knot categorification problem” is to find a uniform description of this theory, for all gauge groups, which originates from physics. I found...

Mean curvature flow (MCF) is a geometric heat equation where a submanifold evolves to minimize its area. A central problem is to understand the singularities that form and what these imply for the flow. I will talk about joint work with Toby Colding...