Video Lectures

The rigorous derivation of the Vlasov equation from Newtonian mechanics of $N$ Coulomb-interacting particles is still an open problem. In the talk I will present recent results, where an $N$-dependent cutoff is used to make the derivation possible...

In this talk, I would like to explain my joint work with Weiwei Wu about understanding projective Dehn twist using Lagrangian cobordism.

This is a part of my joint work with Oh-Ohta-Ono and is a part of project to rewrite the whole story of virtual fundamental chain in a way easier to use. In general we can construct virtual fundamental chain on (basically all) the moduli space of...

Beyond Endoscopy is the proposal by Langlands for using the trace formula to attack the Principle of Functoriality. Many of the problems at this (early) stage concern the geometric terms in the trace formula. Most immediate perhaps is to extend...

Asymptotics for the distribution of Hecke eigenvalues in families of automorphic forms are useful to study families of L-functions, provided one has a sufficiently good estimate for the error term of the asymptotic. I want to present ongoing joint...

This is a survey of how the existing theories of L-functions are in agreement with Braverman-Kazhdan/Ngo's construction of L-functions which generalizes that of Godement-Jacquet. One hopes that such insights may play a role in understanding the...