## Mathematical Physics and Harmonic Analysis Seminar

**Date:** November 15, 2019

**Time:** 1:50PM - 2:50PM

**Location:** BLOC 628

**Speaker:** Sohrab Shahshahani, UMass Amherst

**Title:** *Asymptotic stability of harmonic maps on the hyperbolic plane under the Schrodinger maps evolution*

**Abstract:** We consider the Cauchy problem for the Schrodinger maps evolution when the domain is the hyperbolic plane. An interesting feature of this problem compared to the more widely studied case on the Euclidean plane is the existence of a rich new family of finite energy harmonic maps. These are stationary solutions, and thus play an important role in the dynamics of Schrodinger maps. The main result is the asymptotic stability of (some of) such harmonic maps under the Schrodinger maps evolution. More precisely, we prove the nonlinear asymptotic stability of a finite energy equivariant harmonic map Q under the Schrodinger maps evolution with respect to non-equivariant perturbations, provided that Q obeys a suitable linearized stability condition. This is joint work with Andrew Lawrie, Jonas Luhrmann, and Sung-Jin Oh.