# Video Lectures

### Towards a modular "2 realizations" equivalence

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...

### On Chen’s recent breakthrough on the Kannan-Lovasz-Simonovits conjecture and Bourgain's slicing problem - Part III

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...

### Conformal Colliders Meet the LHC

Ian Moult

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-Schoen energy revisited

Nicola Gigli

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...

### On Quantum Fields and Sphere Packings

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...

### Twisted topological tangles or: the knot theory of knitting

Elisabetta Matsumoto

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...

We revisit the computation of string correlation functions in AdS3 with pure NS-NS flux from a worldsheet point of view. These correlators contain all the perturbative information about the spacetime CFT and the existence of winding strings in AdS3...

### On the canonical, fpqc and finite topologies: classical questions, new answers (and conversely)

Yves André

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...

### Khovanov Homology from Mirror Symmetry

Mina Aganagic

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 in high co-dimension

William Minicozzi

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...