# Video Lectures

### The Value of Errors in Proofs

A few months ago, a group of theoretical computer scientists posted a paper on the Arxiv with the strange-looking title "MIP* = RE", impacting and surprising not only complexity theory but also some areas of math and physics. Specifically, it...

### Graph comparison

Anton Petrunin

I will survey results related to graph comparison; graph comparison is a certain type of restriction on a metric spaces which is encoded by a given graph.

### The Value of Errors in Proofs

A few months ago, a group of theoretical computer scientists posted a paper on the Arxiv with the strange-looking title "MIP* = RE", impacting and surprising not only complexity theory but also some areas of math and physics. Specifically, it...

### Rainbow structures, Latin squares & graph decompositions

Benny Sudakov

A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours.  The study of rainbow subgraphs goes back to the work of Euler on Latin squares in the 18th century.  Since then rainbow structures were the focus of...

### Twisted generating functions and the nearby Lagrangian conjecture

Sylvain Courte

I will explain the notion of twisted generating function and show that a closed exact Lagrangian submanifold LL in the cotangent bundle of MM admits such a thing. The type of function arising in our construction is related to Waldhausen's tube space...

### Selmer groups and a Cassels-Tate pairing for finite Galois modules

Alexander Smith

I will discuss some new results on the structure of Selmer groups of finite Galois modules over global fields. Tate's definition of the Cassels-Tate pairing can be extended to a pairing on such Selmer groups with little adjustment, and many of the...

Elijah Bodish

### The affine Hecke category is a monoidal colimit

James Tao

We will discuss the following theorems concerning colimits taken in the infinity-category of monoidal DG-categories. (No familiarity with infinity-categories will be required or assumed.) The affine Hecke category is the monoidal colimit of its...

### Norm stability in the unitary case from Voiculescu to Gromov-Lawson

Shmuel Weinberger

This expository talk will try to bridge the first examples of "almost commuting" unitary matrices that are not almost "commuting unitaries" due to Voiculescu to a more sophisticated and very beautiful construction of examples by Gromov and Lawson in...

### Introduction to Laplacian Linear Systems for Undirected Graphs

This talk gives an introduction on how to quickly solve linear systems where the matrix of the system is the Laplacian matrix of any undirected graph. No prior familiarity with optimization is assumed. In the process, we will cover:

• what positive...