Video Lectures

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...

The no-boundary state in de Sitter offers a compelling framework for specifying the initial conditions of our universe. Many (but famously not all) features of the state agree beautifully with empirical observations and have served as a foundation...

The Poisson summation conjecture of Braverman-Kazhdan, L. Lafforgue, Ngo, and Sakellaridis is an ambitious proposal to prove analytic properties of quite general Langlands L-functions using vast generalizations of the Poisson summation formula. In...

Many geometric spaces carry natural collections of special submanifolds that encode their internal symmetries. Examples include abelian varieties and their sub-abelian varieties, locally symmetric spaces with their totally geodesic subspaces, period...

I will motivate current work in weak gravitational lensing with cosmic and astrophysical puzzles. The evolution of dark energy, the growth of structure and feedback from supermassive black holes are some of the debated questions. I will describe how...

The Schwarzschild-de Sitter solution can be used to compute the Hartle-Hawking wavefunction of the universe on a spatial circle times a sphere. Its norm can be evaluated in the semiclassical limit and compared to the on-shell action of the Euclidean...