Video Lectures

I will discuss the difficult problem of proving reasonable bounds in the multidimensional generalization of Szemer\’edi’s theorem and describe a proof of such bounds for sets lacking nontrivial configurations of the form $(x,y), (x,y+z), (x,y+2z),...

Following the collision of two compact objects, an accretion disk forms and from it matter is ejected that sources the universe's heavy elements and that is observable as a kilonova. The amount of ejecta, the types of elements that form, and the...

We will discuss the price of the quantum error correcting codes, defined as the number of physical qubits needed to reconstruct whether a given operator has been acted upon the thermal state or not. By thinking about reconstruction via quantum...

We will discuss some old and new results concerning the long-time behavior of solutions to the two-dimensional incompressible Euler equations.  Specifically, we discuss whether steady states can be isolated, wandering for solutions starting nearby...

One of the central problems of coding theory is to determine the trade-off between the amount of information a code can carry (captured by its rate) and its robustness to resist message corruption (captured by its distance). On the existential side...

Understanding the behavior of multi-player (multi-prover) games under parallel repetition is an important problem in theoretical computer science.

In a k-player game G, a referee chooses questions (x1,...,xk) from a (publicly known) distribution...

Modern theoretical investigations into the nature of spacetime are revealing that quantum entanglement plays a crucial role for resolving several long standing puzzles. Black holes have been central to these investigations. Quantum models for black...

In this talk, I want to show that in the planar circular restricted three body problem there are infinitely many symmetric consecutive collision orbits for all energies below the first critical energy value.  By using the Levi-Civita regularization...

Liouville field theory was introduced by Polyakov in the eighties in the context of string theory. Liouville theory appeared there under the form of a 2D Feynman path integral, which can be thought of as a measure (or expectation value) over the...

We discuss the existence problem of constant Chern scalar curvature metrics on a compact complex manifold. We prove a priori estimates for these metrics conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the...