Video Lectures

We discuss some properties of a pseudo-metric on the contactomorphism group of a strict contact manifold M induced by the maximum/minimum of Hamiltonians. We show that it is non-degenerate if and only if M is orderable and that its metric topology...

The lecture introduces the audience to the process of interaction of one of the most important Middle Eastern Church traditions, Syriac Christianity, with the Holy City and the Holy Land. Even if scholars have often argued that the late antique...

Can we reconstruct a function by knowing only a subset of its values and a subset of the values of the function's Fourier transform?

How many values do we need to know for such a reconstruction? Can we interpolate a given subset of values? What are...

I will give an introduction to the problem of sampling from a strongly log-concave density on Euclidean space through the lens of convex optimization.  In particular, I will focus on the interpretation, due to Jordan, Kinderlehrer, and Otto, of the...

The iconic spiral arms that decorate the disks of massive galaxies (like our own Milky Way) have been studied observationally and theoretically since they were first recorded 180 years ago, nevertheless the exact details of their nature remains...

The finite field Kakeya problem asks about the size of the smallest set in (F_q)^n containing a line in every direction.  Raised by Wolff in 1999 as a ‘toy’ version of the Euclidean Kakeya conjecture, this problem is now completely resolved using...

Chaidez and Edtmair have recently found the first examples of dynamically convex domains in R4 that are not symplectomorphic to convex domains (called symplectically convex domains), answering a long-standing open question. In this talk we shall...

In 1948, Shannon used a probabilistic argument to show the existence of codes achieving channel capacity. In 1954, Muller and Reed introduced a simple deterministic code construction, conjectured shortly after to achieve channel capacity. Major...

Submanifolds with intrinsic Lipschitz regularity in Carnot groups (i.e.,
stratified groups endowed with a sub-Riemannian structure) can be
introduced using the theory of intrinsic Lipschitz graphs started years
ago by B. Franchi, R. Serapioni and F...

I will talk about the invariants of topologically ordered states of quantum lattice systems that generalize Berry classes and can be defined for any gapped state in any dimension. The equivariant version of such invariants unifies and generalizes...