Video Lectures

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...

Convex integration and the holonomic approximation theorem are two well-known pillars of flexibility in differential topology and geometry. They each seem to have their own flavor and scope. The goal of this talk is to bring new perspective on this...

Beltrami fields, that is vector fields on $\mathbb R^3$ whose curl is proportional to the field, play an important role in fluid mechanics and magnetohydrodynamics (where they are known as force-free fields). In this lecture I will review recent...

Abstract 1: Measurements of the Hubble constant (H0) as determined via the Cepheid-supernovae distance ladder appear to provide strong evidence for physics beyond LCDM. However, in the Carnegie Chicago Hubble Program (CCHP), we used the Tip of the...

 I will discuss a remarkable generalization of Mather’s theorem by Thurston that relates the identity component of diffeomorphism groups to the classifying space of Haefliger structures. The homotopy type of this classifying space played a...

We discuss the problem of extending local deformations of solutions to open partial differential relations to global deformations and formulate conditions under which such extensions are possible. Among others these results are applied to study...

We give a new proof of the fact that the parallel repetition of the (3-player) GHZ game reduces the value of the game to zero polynomially quickly.  That is, we show that the value of the n-fold parallel repetition of the GHZ game is at most n^{-...

We prove the equivalence of Eliashberg overtwisted $h$—principle and  the Eliashberg-Mishachev classification of contact structures in the tight $3$-ball. I.e. we prove that simple algebraic topology computations takes us from one result to the...