Video Lectures

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...

video lecture

Morrey Saces and Regularity for Yang-Mills Higgs Equations

December 07, 2018

Karen Uhlenbeck

We start with background on regularity theory for the equations of gauge theory. Morrey spaces arise naturally from monotinicity theorems in dimensions greater than 4. Our main technical result is that functions in a Morrey space which satisfy an...

video lecture

Slopes in eigenvarieties for definite unitary groups

December 06, 2018

Lynnelle Ye

The study of eigenvarieties began with Coleman and Mazur, who constructed the first eigencurve, a rigid analytic space parametrizing $p$-adic modular Hecke eigenforms. Since then various authors have constructed eigenvarieties for automorphic forms...

video lecture

Quantum Chaos and Effective Field Theory

December 05, 2018

Felix Haehl

Please Note: This workshop is not open to the general public, but only to active researchers.

This workshop will focus on quantum aspects of black holes, focusing on applying ideas from quantum information theory.

This meeting is sponsored by the “It...

video lecture

Global results related to scalar curvature and isoperimetry

December 04, 2018

Otis Chodosh

I will first survey some recent progress on global problems related to scalar curvature and area/volume, focusing in particular on scale breaking phenomena in such problems. I will then discuss the role of the Hawking mass in the resolution of this...

video lecture

Mean action of periodic orbits of area-preserving annulus diffeomorphisms

December 03, 2018

Morgan Weiler

An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while...

video lecture

Recent Progress on Zimmer's Conjecture

December 03, 2018

David Fisher

Lattices in higher rank simple Lie groups are known to be extremely rigid. Examples of this are Margulis' superrigidity theorem, which shows they have very few linear represenations, and Margulis' arithmeticity theorem, which shows they are all...

video lecture

Branched conformal structures and the Dyson superprocess

November 30, 2018

Govind Menon

In the early 1920s, Loewner introduced a constructive approach to the Riemann mapping theorem that realized a conformal mapping as the solution to a differential equation. Roughly, the “input” to Loewner’s differential equation is a driving measure...

video lecture

The Lucky Logarithmic Derivative

November 29, 2018

Will Sawin

We study the function field analogue of a classical problem in analytic number theory on the sums of the generalized divisor function in short intervals, in the limit as the degrees of the polynomials go to infinity. As a corollary, we calculate...

video lecture

Bubbling theory for minimal hypersurfaces

November 27, 2018

Ben Sharp

We will discuss the bubbling and neck analysis for degenerating sequences of minimal hypersurfaces which, in particular, lead to qualitative relationships between the variational, topological and geometric properties of these objects. Our aim is to...