Abstract

Schrodinger maps are solutions of a highly nonlinear PDE with geometric structure arising from the constraint that the solutions must lie on a given target manifold. For example, the well-known Landau-Lifshitz equation, describing ferromagnetism, is the special case in which the target is the sphere. PDE techniques that incorporate the geometry allow us to prove both the existence and uniqueness of Schrodinger maps.

To prove existence, we approximate the Schrodinger map equation with a sequence of wave map equations whose speeds of propagation tend to infinity. Using energy estimates, we then construct a Schrodinger map by taking the limit of solutions to the approximating wave map problems. Finally, by using parallel trans

WEDNESDAY, October 27, 2005
Time: 4:30 P.M.
Location: DH 2302