Video Lectures

The study of Turán numbers of graphs and hypergraphs is a rich problem in extremal combinatorics. The Turán problem asks, given a fixed forbidden (hyper)graph F, what is the maximum number of edges in an F-free (hyper)graph in terms of the number of...

Entanglement Bootstrap is a research program to understand and extract the universal data of quantum many body states from local entanglement information.  Since this universal data is usually encoded in a quantum field theory, the program can teach...

We describe the obstruction to lift Frobenius on certain Shimura varieties and apply this to the theory of companion forms for classical modular forms (Gross, Coleman-Voloch, Faltings-Jordan) and also in higher dimension.

Since Hironaka's famous resolution of singularities in characteristics zero in 1964, it took about 40 years of intensive work of many mathematicians to simplify the method, describe it using conceptual tools and establish its functoriality. However...

High-dimensional expanders (HDX) are a generalization of expander graphs which have seen various applications in coding theory, PCPs, pseudorandomness, derandomization, approximate sampling, and beyond. One technique for proving a complex is an HDX...

This talk has two parts. In the first, I will discuss a well-known Lorentzian axiomatic framework in which quantum gravity theorems can be rigorously established, with the quantum extremal surface prescription as a central highlight. I will describe...

In AdS/CFT, the black hole singularity is encoded as a divergence in a certain analytic continuation of the two-point function. This divergence corresponds to a null geodesic that bounces off the singularity. In this talk, we will study the fate of...

We study the double cone geometry proposed by Saad, Shenker, and Stanford in de Sitter space. We demonstrate that with the inclusion of static patch observers, the double cone leads to a linear ramp consistent with random matrix behavior. This ramp...

The two-point correlation function of a massive field, measured along an observer's worldline in de Sitter (dS), decays exponentially in time. Meanwhile, every dS observer is surrounded by a horizon and the holographic interpretation of the horizon...