Video Lectures

I will introduce the topic of heavy multiquark states, with special attention to the current theoretical and experimental status. I will first review the available experimental information and then discuss them in the context of the two most likely...

The "c-principle" is a cousin of Gromov's h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that  for the MT-theorem, when the base dimensions is not equal four, only the mildest cobordisms...

We describe a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in...

Singularities of smooth maps are flexible: there holds an h-principle for their simplification. I will discuss an analogous h-principle for caustics, i.e. the singularities of Lagrangian and Legendrian wavefronts. I will also discuss applications...

In this talk we will show how to construct finite dimensional families of non-steady solutions to the Euler equations, existing for all time, and exhibiting all kinds of qualitative dynamics in the phase space of divergence-free vector fields, for...

We introduce Lefschetz fibration structures on the Milnor fibers of simple-elliptic and cusp singularities in complex three variables, whose regular fibers are diffeomorphic to the 2-torus. We know two ways to construct them and explain h-principle...

Magnetism has been in the forefront in our understandings of protoplanetary disks (PPD) and planet formation. With the prevalence of disk substructures, a major observational revolution over the past few years, PPDs are now considered as “planet...

The field of continuous combinatorics studies large (dense) combinatorial structures by encoding them in a "continuous" limit object, which is amenable to tools from analysis, topology, measure theory, etc. The syntactic/algebraic approach of "flag...