Video Lectures

I will explain how Gromov-Witten theory can be used to prove that certain projective hypersurfaces are symplectically irrational, that is, cannot be related to projective space by symplectic blow-ups, blow-downs, and deformations.

The topology of Lagrangian submanifolds in the standard symplectic vector space 𝐶𝑛

is a fundamental yet poorly understood problem in symplectic topology. A related question, known as Maslov class rigidity, concerns constraints on the Maslov classes...

One of the problems in the OpenAI drop last month, the unique games conjecture has been a major problem in theoretical computer science, pertaining to PCPs and hardness of approximation. I will talk about the field, the background, and a little bit...

We discuss the construction of an Euler system for the triple product, the p-adic Galois representation 𝑉=𝑉1𝑥𝑉2𝑥𝑉3, where 𝑉1,𝑉2,𝑉3 are the 2-dimensional representations attached to cuspforms 𝑓1,𝑓2,𝑓3. Applications include new cases of the Bloch—Kato...

In this talk, we introduce a non-linear symplectic capacity for four-dimensional Euclidean domains 𝑋, known as the shape invariant of 𝑋, which encodes the embeddability of Lagrangian tori into 𝑋. We present a computational framework for this...

In this learning seminar talk, I will explain the local picture underlying the technique of defining integer-valued curve counts, known as the FOP perturbation (named after Fukaya-Ono and B. Parker). The problem is indeed very simple: given a finite...

A classical problem in harmonic analysis is to understand how the mass of Laplace eigenfunctions distributes as their parameters tend to infinity. In this talk, I will consider this problem on arithmetic hyperbolic surfaces obtained as quotients of...

For a closed manifold (𝑀,𝑔) with isometry group, 𝐺, we will discuss the construction of 𝐺

-invariant minimal hypersurfaces. Pitts-Rubinstein initiated the program to construct such hypersurfaces via min-max methods. The community has made significant...