Seminar on Microlocal Analysis and Applications

A new approach to the nonlinear Schrödinger equation

Abstract

With 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.

Speaker

I am currently a Professor and Associate Director of Research in the Mathematical Sciences Institute at ANU. My PhD was done at MIT in the period 1990-94. After that, I did a 2 year postdoc at Stanford University, and then I moved to ANU, initially as an ARC Postdoctoral Fellow. I became an ARC Research Fellow during 1999-2004, and a Future Fellow during 2010-2014. I was elected to the Australian Academy of Science in 2013.

My research interests are in spectral and scattering theory, partial differential equations, microlocal analysis and semiclassical analysis. Specific recent topics include wave equations with rough coefficients, analysis of resolvents and heat kernel on complete Riemannian manifolds, Fredholm theory for non-elliptic operators and nonlinear dispersive equations.