Video Lectures

The algebraic structure of various groups of homeomorphisms and diffeomorphisms was studied extensively in the 1960s and 1970s, when it was shown that these groups are (mostly) simple. A notable open case concerned the group of area-preserving...

A surprising property of the cohomology of locally symmetric spaces is that Hecke operators can act on multiple cohomological degrees with the same eigenvalues. In a series of papers, Venkatesh and his collaborators proposed an arithmetic reason for...

After ten years of gravitational-wave observations with the LIGO–Virgo–KAGRA interferometers, over 200 signals from merging black hole binaries have been detected, bringing us closer to understanding how these systems form. Addressing this question...

Differential Galois groups are algebraic groups that describe symmetries of some systems of differential equations. The solutions considered can live in any differential field and thus a natural framework to consider such symmetries is the setting...

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...