Video Lectures

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...

Fast radio bursts (FRBs) are a big puzzle in astrophysics. Observational evidence and theoretical arguments connect FRBs to magnetars, yet their emission mechanism is not established. One popular picture resembles pulsars on steroids, with radio...

In this talk, I will present an upper bound for the Lagrangian capacity of a Liouville domain with finite Gutt–Hutchings capacities. We prove that the Lagrangian capacity of every convex or concave toric domain, in arbitrary dimension, equals its...

This talk will present and scrutinize certain structures underlying what we usually call the semiclassical limit of AdS/CFT: how families of CFTs develop gravitational regimes at large N; how their exact high-energy spectra compare to black hole and...

The simplest kind of Gromov-Witten invariants produce the (very) small quantum connection, which is a connection in one variable with a regular singularity at origin. I will discuss a conjecture which predicts that for a smooth complex Fano variety...

Although Lewis Hyde's The Gift is primarily concerned with the status of works of art, he does devote part of a chapter to arguing that scientific research functions as a gift economy: the scientist (ideally) contributes new knowledge as a shared...

There are several ways to define when two subsets of 𝑅2𝑛 are symplectically equivalent. We will discuss when some of these notions coincide and present somewhat surprising examples showing that they need not coincide in general. Based on joint work...

A hypersurface in a contact manifold comes equipped with a natural dynamical system, called the characteristic foliation. Special cases include the suspension flow of a contactomorphism and the Liouville flow on a Liouville manifold. In this talk, I...

Since the discovery of the Amplituhedron in 2013, positive geometry has attracted considerable interest in both physics and mathematics, revealing connections between scattering amplitudes and cosmological correlators on the one hand, and...