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...

Powerful extragalactic radio sources hosted in galaxies come in all shapes, sizes, powers, and presumably ages.  What might a young or nascent powerful radio source look like?  The class of compact powerful extragalactic radio sources are defined to...

A new class of phase transitions has been recently studied in quantum many-body systems that are subject to measurements but not otherwise open to any external decoherence.  This phase transition arises from a competition between scrambling dynamics...

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...

Lightray operators have played an important role in numerous recent developments in conformal field theory. These operators, and their associated operator product expansion (OPE), also play a central role in collider experiments, where they govern...

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...

Developments in fundamental physics over the last century have led to the formulation of a universal language successfully describing Nature from the subatomic scale to the universe as a whole. This language is known as quantum field theory. In...