Video Lectures

An evolving surface is a mean curvature flow if the normal component of its velocity field is given by the mean curvature. First introduced in the physics literature in the 1950s, the mean curvature flow equation has been studied intensely by...

New results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field are presented. This includes a family of double well potentials containing examples for which the low-energy eigenvalue splitting...

We travel the years in order to understand the relationship between Nilpotency and Riemannian geometry: including Gromov's almost flat theorem for manifolds with bounded curvature and Fukaya-Yamaguchi's almost nilpotency of spaces with lower...

In quantum complexity theory, QMA and QCMA represent two different generalizations of NP. Both are defined as sets of languages whose Yes instances can be efficiently checked by a quantum verifier that is given a witness. With QMA the witness can be...

Kaledin established a Cartier isomorphism for cyclic homology of dg-categories over fields of characteristic p, generalizing a classical construction in algebraic geometry. In joint work with Paul Seidel, we showed that this isomorphism and related...

In this talk, I will present several a priori interior and boundary trace estimates for the 3D incompressible Navier–Stokes equation, which recover and extend the current picture of higher derivative estimates in the mixed norm. Then we discuss the...

Quasars at cosmic dawn are powerful probes to the formation and growth of early supermassive black holes in the universe, their connections to high-redshift galaxy and structure formation, and the evolution of the intergalactic medium at the epoch...

Expander graphs are a staple of theoretical computer science. These are graphs which are both sparse and well connected. They are simple to construct and modify. Therefore they are a central gadget in numerous applications in TCS and combinatorics...

Muon colliders offer a unique path to multi-TeV, high-luminosity lepton collisions. Muon collisions with a center-of-mass energy of 10 TeV or above would offer significant discovery potential where the constituent collision energies exceed those of...

Ohta described the ordinary part of the 'etale cohomology of towers of modular curves in terms of Hida families. Ohta's approach crucially depended on the one-dimensional nature of modular curves. In this talk, I will present joint work with Chris...