# 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 classication, in the spirit of recent work by Duyckaerts, Kenig, and Merle, of all degree 1 solutions with energy below *three times* the energy of \(Q\).