Abstract: 

I will discuss a new methodology for proving small data scattering for the nonlinear Schrödinger equation, which avoids the use of Strichartz estimates, and uses instead methods from microlocal analysis.  This methodology is flexible and can in principle be applied to massive wave propagation as in the Klein-Gordon or massive Dirac equations.  This is joint work with Andrew Hassell and Sean Gomes and with Dean Baskin and Moritz Doll.