# Video Lectures

We will discuss some results on high-degree varieties designed to expand the reach of the polynomial method and explain their applications in incidence geometry.

Irreducibility of random polynomials of large degree has been studied recently in works by several authors (in particular by Bary-Soroker, Kozma, Koukoulopoulos and by Varju and myself). We study analogous problems in the setting of word maps in...

Radiation emitted from evaporating black holes is highly mixed, at least for times prior to the so-called "Page time." Usually, the quantum state of the radiation is then treated as void of information. I will discuss two ways in which this early...

What is the symplectic analogue of being convex? We shall present different ideas to approach this question. Along the way, we shall present recent joint results with J.Dardennes and J.Zhang on monotone toric domains non-symplectomorphic to convex...

Tate reformulated the theory of the Riemann zeta function and its functional equation as the Mellin shadow of the Fourier transform on a certain space of function on the adeles. Conjecturally, Langlands' general automorphic L-functions and their...

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...