# Video Lectures

### Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d > 2

For the Bargmann--Fock field on Rd with d>2, we prove that the critical level lc(d) of the percolation model formed by the excursion sets {f?l} is strictly positive. This implies that for every l sufficiently close to 0 (in particular for the nodal...

We will discuss embeddings of manifolds with a view towards applications in contact and symplectic category.

A locally testable code (LTC) is an error correcting code that admits a very efficient membership test. The tester reads a constant number of (randomly - but not necessarily uniformly - chosen) bits from a given word and rejects words with...

Despite the fact that the 3-body problem is an ancient conundrum that goes back to Newton, it is remarkably poorly understood, and is still a benchmark for modern developments. In this talk, I will give a (very) biased account of this classical...

A locally testable code (LTC) is an error correcting code that admits a very efficient membership test. The tester reads a constant number of (randomly - but not necessarily uniformly - chosen) bits from a given word and rejects words with...

In various areas of mathematics there exist "big fiber theorems", these are theorems of the following type: "For any map in a certain class, there exists a 'big' fiber", where the class of maps and the notion of size changes from case to case.

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After surveying some important consequences of the property of bounded generation (BG) dealing with SS-rigidity, the congruence subgroup problem, etc., we will focus on examples of boundedly generated groups. We will prove that every unimodular (n×n...

A fundamental problem in the theory of compressible fluid is to provide a precise description of shock formation and development from smooth initial data. In this talk, I will present recent work in collaboration with Drivas, Shkoller and Vicol on...

A random point process is said to be determinantal if finite subset probabilities correspond to principal minors of some matrix. Determinantal point processes (DPPs) appear in a wide variety of settings, from random matrix theory to combinatorics...