# Analysis Seminar

#### Classification of Large Energy Equivariant Wave Maps

Speaker: Andrew Lawrie, University of Chicago

Location: Warren Weaver Hall 1302

Date: Thursday, November 29, 2012, 11 a.m.

Synopsis:

I will discuss some recent joint work with Raphaël Côte, Carlos Kenig, and Wilhelm Schlag. We consider energy critical 1-equivariant wave maps, $$\mathbb{R}^{1+2} \to \mathbb{S}^{2}$$. This problem admits a unique (up to scaling) harmonic map, $$Q$$, given by stereographic projection.

We show that every topologically trivial (degree 0) solution with energy less than twice the energy of $$Q$$ exists globally in time and scatters. Next we establish a classi cation, in the spirit of recent work by Duyckaerts, Kenig, and Merle, of all degree 1 solutions with energy below three times the energy of $$Q$$.