# Video Lectures

### 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...

### 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...

### 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...

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

This is the second talk in a 3-lecture 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 (a video of the first lecture can be found here:

https://www...

### On the Ising perceptron model

Nike Sun

(This lecture will be self-contained.) In high dimensions, what does it look like when we take the intersection of a set of random half-spaces with either the sphere or the Hamming cube? This is one phrasing of the so-called perceptron problem...

### Kolyvagin's conjecture and higher congruences of modular forms

Naomi Sweeting

Given an elliptic curve E, Kolyvagin used CM points on modular curves to construct a system of classes valued in the Galois cohomology of the torsion points of E. Under the conjecture that not all of these classes vanish, he gave a description for...

### Kazhdan-Lusztig category

Jin-Cheng Guu

The talk introduces the Kazhdan-Lusztig categories of representations of affine Lie algebras

### Probabilistic analysis of random CSPs

Nike Sun

(This lecture is related to the preceding lecture, but I will try to make it self-contained as much as possible.) In this lecture I will elaborate on some of the existing mathematical approaches to the study of random CSPs, particularly involving...