## 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.