Video Lectures

It is convenient to formalize the discussion about Hamiltonian Floer theory using the language of flow categories and bimodules. In this lecture I will explain how to use the notion of "derived orbifold chart lift" of flow categories and bimodules...

In this talk I will present a general framework to establish the stability of  inequalities of the form >= F(u); where L is a positive linear operator and F is a 2-homogeneous nonlinear functional.

We will then see how this framework can be...

I will explain how to generalize Abouzaid-McLean-Smith's construction to Floer moduli spaces. As we need to regularize infinitely many moduli spaces, we need to make choices consistently. We also need to generalize the smoothing theory to the...

A number is called y-smooth if all of its prime factors are bounded above by y. The set of y-smooth numbers below x forms a sparse subset of the integers below x as soon as x is sufficiently large in terms of y. If f_1, …, f_r \in Z[x_1,…,x_s] is a...

We give the first almost-linear time algorithm for computing exact maximum flows and minimum-cost flows on directed graphs. By well known reductions, this implies almost-linear time algorithms for several problems including bipartite matching...

An Anosov flow Φ on a closed 3-manifold M gives rise to a non-Weinstein Liouville structure on V:=[−1,1]×M. Building upon the work of Hozoori, we establish a homotopy correspondence between Anosov flows and certain pairs of contact forms. Moreover...

Noetherianity is a fundamental property of modules, rings, and topological spaces that underlies much of commutative algebra and algebraic geometry. This talk concerns algebraic structures such as the infinite-dimensional polynomial ring K[x_1,x_2...

In contrast to symmetry breaking phases of matter, unconventional phases like spin liquids feature long-range quantum entanglement and relate to the deconfined phases of gauge theories. However, the realization of these states  in materials has...

In interactive coding, Alice and Bob wish to compute some function f of their private inputs x and y. They do this by engaging in a non-adaptive (fixed speaking order, fixed length) protocol to jointly compute f(x,y). The goal is to do this in an...