Stochastic Curvature Driven Flows - Some Results and Questions

I will discuss several mathematical problems related to curvature driven flows arised from interfacial motions in crystal growth. Emphasis will be on stochastic effects. Specific examples of such flows include motion by mean curvature and dendritic crystal growth with Gibbs-Thompson condition. In some cases, noise can be shown to give a selection principle to the evolutions in case of non-uniqueness.