Video Lectures

We will give an overview of some of the developments in recent years dealing with the description of asymptotic states of solutions to semilinear evolution equations ("soliton resolution conjecture").

New results will be presented on damped...

I will discuss several results on abstract homomorphisms between the groups of rational points of algebraic groups. The main focus will be on a conjecture of Borel and Tits formulated in their landmark 1973 paper.

Our results settle this...

I will explain an application of the geometric Satake correspondence (in its derived form due to Bezrukavnikov-Finkelberg) to the study of differential operators on $G$-spaces (for $G$ complex reductive) and its classical version, the study of...

This talk will be an introduction to the methods used in the study of spectral properties of Schroedinger operators with a potential defined via the action of an ergodic transformation. Open problems relating to Lyapunov exponents over a skew shift...

The Random Fourier Features (RFF) method (Rahimi, Recht, NIPS 2007) is one of the most practically successful techniques for accelerating computationally expensive nonlinear kernel learning methods. By quickly computing a low-rank approximation for...

We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained in recent...

Last semester I gave a talk that was a 1-hour condensation of undergrad machine learning. https://www.ias.edu/video/membsem/2017/1127-SanjeevArora . This semester's talk will be a 1-hour treatment of some research directions in theoretical machine...

An error-correcting code is called locally repairable if any coordinate of a codeword can be recovered by accessing only few other coordinates. For locally repairable codes over small alphabets (such as binary), the optimal trade-off between...

Given a measure preserving dynamical system, a real-valued observable determines a random process (by composing the observable with the iterates of the transformation). An important topic in ergodic theory is the study of the statistical properties...

In these lectures, we will explore what insight can be gained into the arithmetic of Galois representations in a given dimension through the geometry of a higher-dimensional locally symmetric space near a boundary component. The starting point for...