Title: What is Second Micrlocalization and what is it good for
Speaker: Fabricio Macia
Speaker Info: Universidad Politécnica de Madrid.
Abstract: We review some recent results on concentration and non concentration properties for solutions to the Schrödinger equation on a compact Riemannian manifold. These results have applications to the study of unique continuation and dispersive effects for Schrödinger flows and to the structure of high-frequency eigenfunctions of the Laplacian. The geometric setting we are interested in is that of compact manifolds (possibly with boundary) whose geodesic flow is completely integrable (or close to completely integrable). The main analytical tool we use is two-microlocal analysis, which appears in a natural way in this setting. I'll present these tools in a simple, yet non-trivial, example in the hope to make them accessible to a wide audience. This is joint work with Nalini Anantharaman.Date: Monday, February 29, 2016