Video Lectures

The incompressible 3D Euler equations have total kinetic energy conservation for smooth (spatially periodic) solutions. In the recent resolution of the Onsager conjecture by Isett, on the other hand, below certain threshold Hölder regularity, Euler...

I will explain a construction of a Legendrian version of embedded contact homology (ECH) for a sutured contact manifold Y along with a collection of Legendrians L contained in the boundary. The chain complex is generated by sets of Reeb orbits and...

I will discuss some questions of interest in neuroscience, seen through the lens of mathematics. No prior knowledge of neuroscience is needed for this talk. Two of the most basic visual capabilities of primates are orientation selectivity, i.e., the...

The degree mantra states that any non-zero univariate polynomial of degree at most d has at most d roots (counted with multiplicity). A generalization of this to the multivariate setting, proved by Dvir-Kopparty-Saraf-Sudan asserts that over any...

In this short talk, I will introduce the notion of n-morphisms between two A-infinity algebras. These higher morphisms are such that 0-morphisms correspond to standard A-infinity morphisms and 1-morphisms correspond to A-infinity homotopies. Their...

A generalization of the cartesian product and the free sum of two convex domains is the p-product operation. We investigate the behavior of symplectic capacities with respect to symplectic p-products, and we give applications related to Viterbo's...

In this talk, I will present two results relating the qualitative dynamics of non-degenerate Hamiltonian isotopies on surfaces to the structure of their Floer complexes.

The first will be a topological characterization of those Floer chains...

Clifford Geertz once quipped: “It is difficult to see what is always there. Whoever discovered water, it was not a fish.” In the same way, seeing familiar environments can prove challenging. Those of us who live our lives in a given space become...

If a monomorphism of abstract groups H↪G induces an isomorphism of profinite completions, then (G,H) is called a Grothendieck pair, recalling the fact that Grothendieck asked about the existence of such pairs with G and H finitely presented and...