Past Events

An interesting problem about eigenfunctions of the Laplace operator is to understand their concentration properties. In the setting of flat tori, Bourgain and Rudnick in a series of papers established uniform bounds for restriction of eigenfunctions to hypersurfaces, as well as several other…

Global existence and scattering for the defocusing nonlinear Schrodinger equation is a celebrated result by Ginibre-Velo in the early 80’s in the strictly energy sub critical case, and Bourgain in 94 in the energy critical case. In the energy super critical setting, the defocusing energy is…

Many recent concordance invariants of knots come from perturbing the differential on a knot homology theory to get a complex with trivial homology but an interesting filtration. I describe the invariant coming from Rasmussen's E(-1) spectral sequence from Khovanov homology in this way, and show…

Abstract: The talk presents an elementary proof of the nonlinear
Landau damping for analytic and Gevrey data, that was first obtained
by Mouhot and Villani and subsequently extended by Bedrossian,
Masmoudi, and Mouhot, coupled with a presentation of echo solutions to
the…

We often convert intricate geometric data (such as counts of
holomorphic disks) into manipulable algebraic data (such as cochain
complexes). In this talk, we discuss joint work with Jacob Lurie
demonstrating that classical invariants can be upgraded to produce far
richer…

We consider the standard first-passage percolation model on $\mathbb{Z}^d$, in which each edge is assigned an i.i.d. nonnegative weight, and the passage time between any two points is the smallest total weight of a nearest-neighbor path between them. Our primary interest is in the empirical…

Suppose you want to solve the eigenvalue problem for the Laplacian in a domain that's close to one you understand well. Can you use that knowledge to understand the spectrum for the new domain? I'll describe Hadamard's formula for the derivative of the eigenvalues, and give some applications.