Video Lectures

Recent breakthroughs in gravitational wave and electromagnetic observations have given better and better insights into black holes and extreme gravity. While one usually thinks of black holes as the unyielding final state of gravitational collapse...

I will talk about the well known relation between cocycles and covers.  Then, I will discuss the relation of cocycle expansion to approximate covers, and finally how these show up in low-soundness PCP agreement tests.

What is the cost of a task if we have to perform it many times? Can we achieve economies of scale? Such "direct-sum problems" play a central role in many areas of mathematics, physics and computer science. Protagonistic problems of this kind are...

In the past decade, we have detected hundreds of gravitational waves, advancing our understanding of the Universe and its governing laws. In this talk, I will present the theoretical models and data analysis tools I have developed for interfacing...

Given a Hamiltonian H∈C∞(S1×M), what is the relationship between the dynamics of the isotopy generated by H and the various Floer-theoretic invariants associated to H? In this talk I will discuss how — in the case where M is a closed surface —one...

LIGO, Virgo, and KAGRA have recently announced the discovery of over 200 new compact binary mergers in low latency during their fourth observing run (O4), a majority of which are stellar-mass binary black hole mergers. The first segment of this run...

We will go in-depth into the proof that for all functions t(n) greater than or equal to n, every multitape Turing machine running in time t can be simulated in space only O(tlogt‾‾‾‾‾√). We will attempt to be completely self-contained. To that end...

The field of unlikely Intersections presents a robust paradigm for problems in which several subjects intermingle: arithmetic, o-minimality, and hodge theory. The goal of this talk will be to introduce some of those connections. My aim is to...

A linear extension of P is a linear ordering compatible with the poset relations. Let p(x less than y) be the probability that x

precedes y in a uniformly random linear extension, and let δ(x,y)=min(p(x less than y),p(y less than x)) and δ(P) be the...

Drawing inspiration from AdS/CFT holography, I will discuss the idea that a static patch in de Sitter space admits a fundamental description based upon standard quantum mechanics. Taking a bottom-up perspective, I compute correlation functions of...