## Jalal Shatah : Nonlinear Dispersive Equations, Invited Lecture

### Schrödinger Maps: Local regularity and singularity formation

### Abstract

Schrödinger Maps are a generalization of the Landau
Lifschitz equations that arise in ferromagnets. We will discuss the
physical meaning of these equations and the equivalence between
Schrödinger Maps and nonlinear Schrödinger equations. We will show how
this equivalence leads to local and global well posedness results. We
will also discuss how singularities might form for data with large
energy.