Video Lectures

We face financial choices every day. From buying a morning coffee, to an online shopping errand in the afternoon, we are asked “Cash, Credit or Debit?” and “Pay Now or Later?”  We occasionally face bigger decisions, like whether to take out a car...

In this talk, I will first discuss some instances in which orbifolds occur in geometry and dynamics, in particular, in the context of billiards and systolic inequalities. Then I will present topological conditions for an orbifold to be a manifold...

A classical theorem of Neukirch and Uchida says that number fields are completely determined by their absolute Galois groups. One might wonder about analogous results for algebraic varieties: in what situations can varieties be “reconstructed” from...

Being a scientist or mathematician can be challenging, and being a minority mathematician even more so. My path hasn’t always been easy, but it has been worthwhile and fulfilling. However, in some sense, I believe that I ended up where I am through...

The twenty years between when I started college and my first visit to IAS saw great changes in opportunities for women in mathematics, as in most professions. Concurrent with this was the birth of a new field of global or geometric analysis. It was...

We consider a Poisson point process on Rd with intensity lambda for d greater than or = 2. On each point, we independently center a ball whose radius is distributed according to some power-law distribution mu. When the distribution mu has a finite d...

The Hofer’s metric dH is a remarkable bi-invariant metric on the group of Hamiltonian diffeomorphisms of a symplectic manifold. In my talk, I will explain a result, obtained jointly with Matthias Meiwes, which says that the braid type of a set of...

The loop equation for circulation PDF as functional of the loop shape is derived from the Hopf equation. This equation is exactly equivalent to the Schrödinger equation in loop space, with viscosity playing the role of Planck's constant. This...

We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the associated regular sets, as well as more general nonlinear functions...

We discuss some recent progress on the model-theoretic problem of classifying the reducts of the complex field (with named parameters and up to interdefinability). The tools we use include Castle’s recent solution of the Restricted Trichotomy...