Video Lectures

I'll be presenting some joint work with Ian Mertz scheduled to appear at STOC 2020. The study of the Tree Evaluation Problem (TEP), introduced by S. Cook et al. (TOCT 2012), is a promising approach to separating L from P. Given a label in [k] at...

I will explain recent joint work proving that the group of compactly supported area preserving homeomorphisms of the two-disc is not a simple group; this answers the ”Simplicity Conjecture” in the affirmative. Our proof uses new spectral invariants...

Let G be a real semi-simple Lie group with an irreducible unitary representation \pi. The non-temperedness of \pi is measured by the parameter p(\pi) which is defined as the infimum of p\geq 2 such that \pi has matrix coefficients in L^p(G). Sarnak...

As deep learning systems become more prevalent in real-world applications it is essential to allow users to exert more control over the system. Exerting some structure over the learned representations enables users to manipulate, interpret, and...

A common situation in Machine Learning is one where training data is not fully representative of a target population due to bias in the sampling mechanism or high costs in sampling the target population; in such situations, we aim to ’transfer’...

In this talk I will describe the notion of "agreement tests" that are motivated by PCPs but stand alone as a combinatorial property-testing question. I will show that high dimensional expanders support agreement tests, thereby derandomizing direct...

A theorist's dream is to show that hard instances/obstructions for an (optimal) algorithm can be used as gadgets to prove tight hardness reductions (which proves optimality of the algorithm). An example of such a result is that of Prasad Raghavendra...

The purpose of the talk is to discuss a class of pseudo-metrics that can be defined on the set of objects of a triangulated category whose morphisms are endowed with a notion of weight. In case the objects are Lagrangian submanifolds (possibly...

This talk surveys the role of margins in the analysis of deep networks. As a concrete highlight, it sketches a perceptron-based analysis establishing that shallow ReLU networks can achieve small test error even when they are quite narrow, sometimes...

In this talk I will describe the notion of "agreement tests" that are motivated by PCPs but stand alone as a combinatorial property-testing question. I will show that high dimensional expanders support agreement tests, thereby derandomizing direct...