AbstractWith collaborators Jesse Gell-Redman and Sean Gomes, we have begun to set up an entirely new framework for tackling the linear and nonlinear Schrödinger equation. I will describe this setup and explain why I believe it is a more powerful framework than existing approaches for studying nonlinear scattering and soliton dynamics.SpeakerI am currently a Professor and Associate Director of R...
In this talk, we discuss the global behaviors of the heat kernel and Green's function one the complete manifold with nonnegative Ricci curvature. we first obtain sharp two-side Gaussian bounds for the heat kernel that sharpens the well-known Li-Yau’s two-side bounds, based on the sharp Li-Yau’s Harnack inequality on such a manifold. As an application, we get the optimal gradient and Laplacian...