Video Lectures

In this talk, I will completely describe the decomposition of an oscillator representation under the tensor embedding of a product of a symplectic and orthogonal group in the case of finite fields via a correspondence proposed by Roger Howe...

Harmonic analysis studies functions on the real line by expanding them as sums of frequencies (exponentials) and analyzing how each term contributes to the whole. In many applications—such as speech recognition—only the low frequencies matter.

Over...

The Hopf-Tsuji-Sullivan theorem states that the geodesic flow on (an infinite) Riemann surface is ergodic iff the Poincare series is divergent iff the Brownian motion is recurrent. Infinite Riemann surfaces can be built by gluing infinitely many...

Complex lines are a class of pseudoholomorphic curves which generalize rational curves. Applications of complex lines to symplectic geometry have been proposed, but they remain poorly understood. In this talk, I will describe a framework for...

Given linear equations over a finite field and under infinity norm, the Short-Integer-Solution (SIS^inf) problem asks to find a solution where each entry is a small number.

In 2021, Chen, Liu, and Zhandry presented an efficient quantum algorithm for...

Over the last decade, large optical time-domain surveys have systematized the discovery of transient flares of emission associated with the tidal disruptions of stars by supermassive black holes. These tidal disruption events (TDEs) are rare events...

By an observation of Efimov and Scholze, Efimov's theorem on the rigidity of localizing motives allows one to construct refinements of topological Hochschild homology and its variants. In this talk, I'll explain how this refinement works, sketch an...

The SAT (Boolean Satisfiability) problem asks whether a given logical formula on n Boolean variables has an assignment of true/false values to its variables that makes the formula true.  The P vs NP question is equivalent to asking whether SAT has a...

Matrix-perturbation bounds quantify how the spectral characteristics of a baseline matrix A change under additive noise E. Classical results, including Weyl’s inequality for eigenvalues and the Davis–Kahan theorem for eigenvectors and eigenspaces...