# Video Lectures

In this short talk, I will discuss an interpolation of FLTZ skeleta mirror to derived equivalent toric varieties. This is joint work with Peng Zhou.

**Speaker's corrections**: 1) The linear map on
page 10 should be sending the basis to 1 and -1...

A classical branching theorem of Weyl describes how an irreducible representation of compact U(n+1)U(n+1) decomposes when restricted to U(n)U(n). The local Gan-Gross-Prasad conjecture provides a conjectural extension to the setting of...

Since the first detection of a gravitational wave event of the merger of two neutron stars in 2017, two more detections in the neutron star mass range have been announced. The first one, GW190425, involved an unusually massive neutron star, the...

Continuation of the previous talk.

The goal of this talk is two-fold. We state a parabolic version of the two realizations theorem and sketch a proof. This version relates Iwahori-constructible sheaves on parabolic affine flag variety to coherent sheaves on a parabolic version of the...

### Why was Connes' embedding conjecture refuted and there are still no known non-hyperlinear groups?

In [MIP*=RE by JNVWY] the authors construct a non-local game that resolves Tsirelson's problem to the negative and by that refute Connes' embedding conjecture (CEC). The game *-algebra (see e.g. [KPS]) enables one to construct a finitely presented *...

Some of the central questions in complexity theory address the amortized complexity of computation (also sometimes known as direct sum problems). While these questions appear in many contexts, they are all variants of the following:

Is the best...

Given a polynomial PP of constant degree in dd variables and consider the oscillatory integral

IP=?[0,1]de(P(?))d?.IP=?[0,1]de(P(?))d?.

Assuming the number dd of variables is also fixed, what is a good upper bound of |IP||IP|? In this talk, I...

String topology, as introduced by Chas and Sullivan 20 years ago, is a product structure on the free loop space of a manifold that lifts the classical intersection product from the manifold to its loop space. I’ll explain how both a product and a...

What edge density of a graph guarantees that that it will contain a particular subgraph? Or one of a given family ?F of subgraphs? The celebrated Erd?s--Stone--Simonovits Theorem characterizes the maximum edge density in ?F-free graphs, in terms of...