Video Lectures

Chernoff's bound states that for any A⊂[N] the probability a random k-tuple s∈([N]k) correctly `samples' A (i.e. that the density of A in s is close to its mean) decays exponentially in the dimension k. In 1987, Ajtai, Komlos, and Szemeredi proved...

In this talk, I'll show that the most natural low-degree test for polynomials over finite fields is ``robust'' in the high-error regime for linear-sized fields. This settles a long-standing open question in the area of low-degree testing, yielding...

Although there are several ways to ''choose a compact hyperbolic surface at random'', putting the Weil-Petersson probability measure on the moduli space of hyperbolic surfaces of a given topology is certainly the most natural. The work of M...

Although there are several ways to ''choose a compact hyperbolic surface at random'', putting the Weil-Petersson probability measure on the moduli space of hyperbolic surfaces of a given topology is certainly the most natural. The work of M...

Chen and Ruan constructed symplectic orbifold Gromov-Witten invariants more than 20 years ago.  In ongoing work with Alex Ritter, we show that moduli spaces of pseudo-holomorphic curves mapping to a symplectic orbifold admit global Kuranishi charts...

An inertial manifold is a positively invariant smooth finite-dimensional manifold which contains the global attractor and which attracts the trajectories at a uniform exponential rate. It follows that the infinite-dimensional dynamical system is...

It is conjectured that every Reeb flow on a closed three-manifold has either two, or infinitely many, simple periodic orbits. I will survey what is currently known about this conjecture. Then, I will try to explain some of the key ideas behind...