Video Lectures

The tasks of finding and randomly sampling solutions of constraint satisfaction problems over discrete variable sets arise naturally in a wide variety of areas, among them artificial intelligence, bioinformatics and combinatorics, and further have...

I will describe the problem of finding the homotopy type of the space of quantum Hamiltonians in dimension d under certain constraints. The common assumptions are that the interactions have finite range and that the ground state is separated from...

The "nearest neighbor (NN) classifier" labels a new data instance by taking a majority vote over the k most similar instances seen in the past. With an appropriate setting of k, it is capable of modeling arbitrary decision rules. Traditional...

In this talk, I'll illustrate how to lift a "small" locally testable code via a high dimensional expander (HDX) to a "large" locally testable code. Given a D-left regular bipartite graph G = ([n], [m], E) and a "small" code C \in {0,1}^D, the Tanner...

In this talk I will discuss some definitions of exponential mixing and other rates of mixing and discuss some of its consequences.

We will discuss the problem of constructing and characterizing uniquely, integral models of Shimura varieties over some primes where non-smooth reduction is expected.

Minimax optimization, especially in its general nonconvex formulation, has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs) and adversarial training. It brings a series of unique...

The unique games conjecture gives a very strong PCP theorem, which, if true, leads to a clean understanding of a broad family of approximation problems. We will describe recent progress on the conjecture and how certain type of expansion and...

A large number of close-in super-Earths have now been discovered. These planets are most likely formed while the proto-planetary disks are still alive, hence the title of this talk. I will report some recent observational results, regarding their...

High dimensional expansion generalizes edge and spectral expansion in graphs to higher dimensional hypergraphs or simplicial complexes. Unlike for graphs, it is exceptionally rare for a high dimensional complex to be both sparse and expanding. The...