Video Lectures

Ramanujan complexes and golden gates in PU(3).

January 09, 2019

In their seminal works from the 80's, Lubotzky, Phillips and Sarnak proved the following two results: (i) An explicit construction of Ramanujan regular graphs. (ii) An explicit method of placing points on the sphere uniformly equidistributed...

video lecture

Distribution of the integral points on quadrics

January 09, 2019

Naser Talebi Zadeh Sardari

Motivated by questions in computer science, we consider the problem of approximating local points (real or p-adic points) on the unit sphere S^d optimally by the projection of the integral points lying on R*S^d, where R^2 is an integer. We present...

video lecture

Bounds in Renormalized Volume for Hyperbolic 3-manifolds

December 18, 2018

Franco Vargas Pallete

Renormalized volume (and more generally W-volume) is a geometric quantity found by volume regularization. In this talk I'll describe its properties for hyperbolic 3-manifolds, as well as discuss techniques to prove optimality results.

video lecture

Barcodes and $C^0$ symplectic topology

December 17, 2018

Sobhan Seyfaddini

Hamiltonian homeomorphisms are those homeomorphisms of a symplectic manifold which can be written as uniform limits of Hamiltonian diffeomorphisms. One difficulty in studying Hamiltonian homeomorphisms (particularly in dimensions greater than two)...

video lecture

Two questions of Landis and their applications

December 14, 2018

Eugenia Malinnikova

We discuss two old questions of Landis concerning behavior of solutions of second order elliptic equations. The first one is on propagation of smallness for solutions from sets of positive measure, we answer this question and as a corollary...

video lecture

The Barbarian Invasions: A Genealogy of the History of Art

December 12, 2018

Eric Michaud

video lecture

Harmonic maps into singular spaces

December 11, 2018

Brian Freidin

In the 90's, Gromov and Schoen introduced the theory of harmonic maps into singular spaces, in particular Euclidean buildings, in order to understand p-adic superrigidity. The study was quickly generalized in a number of directions by a number...

video lecture

Density and equidistribution of minimal hypersurfaces

December 11, 2018

Andre Neves

I will outline the proof of density of minimal hypersurfaces (Irie-Marques-Neves) and equidistribution of minimal hypersurfaces (Marques-Neves-Song).

video lecture

An invitation to tensor networks

December 11, 2018

Michael Walter

Tensor networks describe high-dimensional tensors as the contraction of a network (or graph) of low-dimensional tensors. Many interesting tensor can be succinctly represented in this fashion -- from many-body ground states in quantum physics to the...

video lecture

A matrix expander Chernoff bound

December 10, 2018

Ankit Garg

Chernoff-type bounds study concentration of sums of independent random variables and are extremely useful in various settings. In many settings, the random variables may not be completely independent but only have limited independence. One such...