Video Lectures

In this talk, I will establish a sharp bound on the growth of cuspidal Bianchi modular forms. By the Eichler-Shimura isomorphism, we actually give a sharp bound of the second cohomology of a hyperbolic three manifold (Bianchi manifold) with local...

The absorption method is a very simple yet surprisingly powerful idea coming from extremal combinatorics which allows one to convert asymptotic results into exact ones. It has produced a remarkable number of success stories in recent years with...

Combinatorial Invariance: a Case Study of Pure Math / Machine  Learning Interaction

The combinatorial invariance conjecture is a fascinating conjecture in Representation Theory. Basically it says that certain important polynomials ("Kazhdan-Lusztig...

Recent B-meson data show a reinforced set of deviations from the Standard Model predictions, pointing to violations of lepton flavor universality. I will critically review these data and discuss their theoretical interpretation, including their...

The signature of a knot K in the 3-sphere is a classical  invariant that gives a lower bound on the genera of compact oriented surfaces in the 4-ball with boundary K. We say that K is hyperbolic if its complement admits a complete, finite volume...

Proving a 2009 conjecture of Itai Benjamini, we show:  For any C, there is a greater than 0 such that for any simple random walk on an n-vertex graph G, the probability that the first Cn steps of the walk hit every vertex of G is at most exp[-an]. ...

 In this talk, we will discuss quantum corrections in the gravitational path integral around nearly 1/16-BPS black holes in asymptotically AdS5 x S5 space, dual to heavy operators in N=4 SYM. We argue these quantum corrections come from a version of...

I will talk about an ongoing project that explores the construction of high dimensional Legendrian spheres from supporting open books and contact structures. The input is a Lagrangian disk filling of a Legendrian knot in the binding. We try to...

I will explain the construction of a new class of Liouville domains that live in a complex torus of arbitrary dimension, whose boundary dynamics encodes information about the singularities of a toric compactification. The primary motivation for this...