# Upcoming Events

The Fourier transform has become an indispensable tool in analysis for studying a wide range of phenomena. This talk will review the basic properties of the Fourier transform and its use in studying the solutions of linear constant-coefficient PDEs. Once the basic results have been established,…

Classical theta series are generating functions for counting vectors in a lattice. They turn out to have a miraculous symmetry property called modularity, which is proved by some simple (by modern standards) Fourier analysis. Kudla discovered analogs of theta series in arithmetic geometry,…

The Averaging process (a.k.a. repeated averages) is a mass redistribution model over the vertex set of a graph. Given a graph G, the process starts with a non-negative mass associated to each vertex. The edges of G are equipped with Poissonian clocks: when an edge rings, the masses at the two…

In this joint work with Filip Zivanovic, we construct symplectic cohomology for a class of symplectic manifolds that admit C*-actions and which project equivariantly and properly to a convex symplectic manifold. The motivation for studying these is a large class of examples known as Conical…

Abstract

People study higher Teichmuller theory and using several invariants, one tries to characterize the representations. We give a unifying formula between (Atiyah-Patodi-Singer) signature, Toledo invariant and rho invariant for the surface group (with boundary) representations into Hermitian…

Abstract: When studying the late-time asymptotics of solutions to the (linearised) Einstein equations in gravitational collapse, a key conceptual difficulty is that we have no direct physical understanding on what to assume on initial data.

In this talk (based on joint work with D. Gajic…

Diffusion of new products is a classical problem in Marketing, where it has been extensively studied using compartmental Bass models. These compartmental models implicitly assume that all individuals are homogeneous and connected to each other. To relax these assumptions, one can go back to the…

We show that there exists a quantity, depending only on $C^0$ data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the $C^0$ sense…