Video Lectures

An introduction to affine Grassmanians and the geometric Satake equivalence

October 14, 2020

Jize Yu

This is the first talk in a series of three talks towards understanding Bezrukavnikov-Finkelberg's derived geometric Satake equivalence. In this talk, we recall the geometry of equal characteristic affine Grassmannians and some of the ingredients of...

video lecture

Origins of Structure in Inner Planetary Systems

October 13, 2020

Ruth Murray-Clay

Why do many stars host close-in chains of super-Earths? Why are eccentric gas giants found in some inner planetary systems? What determines which of these outcomes will occur around a particular star? I will present a possible framework for...

video lecture

Arithmetic progressions and spectral structure

October 13, 2020

Thomas Bloom

How dense can a set of integers be while containing no three-term arithmetic progressions? This is one of the classical problems of additive combinatorics, and since the theorem of Roth in 1953 that such a set must have zero density, there has been...

video lecture

Compressible Quantum Matter: General Constraints, Emergent Symmetries, and Anomalies

October 12, 2020

Senthil Todadri

I will discuss properties of phases of matter in systems with a global U(1) symmetry and a (possibly discrete) translation symmetry. The low energy theory of such systems is strongly constrained by these symmetries. I will give a framework to...

video lecture

Towards universality of the nodal statistics on metric graphs

October 12, 2020

Lior Alon

The study of nodal sets of Laplace eigenfunctions has intrigued many mathematicians over the years. The nodal count problem has its origins in the works of Strum (1936) and Courant (1923) which led to questions that remained open to this day. One...

video lecture

Stability, non-approximated groups and high-dimensional expanders

October 12, 2020

Alexander Lubotzky

Several well-known open questions, such as: "are all groups sofic or hyperlinear?", have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in...

video lecture

Explicit near-fully X-Ramanujan graphs

October 12, 2020

Xinyu Wu

In this talk I will introduce constructions of finite graphs which resemble some given infinite graph both in terms of their local neighborhoods, and also their spectrum. These graphs can be thought of as expander graphs with local constraints in a...

video lecture

Parameters in indexed homology

October 09, 2020

Simon Cho

Motivated by thematic similarities between persistent homology and magnitude homology, we describe a simplicial construction associated to a metric space. This construction is determined by (apart from the metric space itself) a choice of two...

video lecture

Symplectic Topology

October 09, 2020

Lev Buhovsky

The Arnold conjecture about fixed points of Hamiltonian diffeomorphisms was partly motivated by the celebrated Poincare-Birkhoff fixed point theorem for an area-preserving homeomorphism of an annulus in the plane. Despite the fact that the Arnold...

video lecture

Representations of p-adic groups and applications

October 08, 2020

Jessica Fintzen

The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the Langlands program is the...