Video Lectures

Multiplicative chaos is the general name for a family of probabilistic objects, which can be thought of as the random measures obtained by taking the exponential of correlated Gaussian random variables. Multiplicative chaos turns out to be closely...

Large sieve inequalities are useful and flexible tools for understanding families of L-functions.  The quality of the bound is one measure of our understanding of the corresponding family.  For instance, they may directly give rise to good bounds...

I will survey recent progress on understanding the value distribution of zeta and L-functions.  In particular I will discuss the problem of moments of the zeta function on the critical line, and central  values of L-functions, where the last twenty...

On April 6, 1972 a young graduate student named Hugh Montgomery and the world-renowned mathematical physicist Freeman Dyson had a conversation in the tearoom at the Institute for Advanced Study which led to a fusion of two disparate fields and an...

Relative symplectic cohomology is a Floer theoretic invariant associated with compact subsets K of a closed or geometrically bounded symplectic manifold M. The motivation for studying it is that it is often possible to reduce the study of global...

Gromov-Witten invariants for a general target are rational-valued but not necessarily integer-valued. This is due to the contribution of curves with nontrivial automorphism groups. In 1997 Fukaya and Ono proposed a new method in symplectic geometry...

Homeomorphism is called contact if it can be written as C0-limit of contactomorphisms. The contact version of Eliashberg-Gromov rigidity theorem states that smooth contact homeomorphisms preserve contact structure. Submanifold L of a contact...

In this talk, I will state a conjecture giving a formula for the Lagrangian capacity of a convex or concave toric domain. First, I will explain a proof of the conjecture in the case where the toric domain is convex and 4-dimensional, using the Gutt...

We show that Viterbo‘s conjecture (for the EHZ-capacity) for convex Lagrangian products in ℝ4 holds for all Lagrangian products (any trapezoid in ℝ2) x (any convex body in ℝ2). Moreover, we classify all equality cases of Viterbo’s conjecture within...