Invariants of singularities via Frobenius -- Mircea Mustaţă

The invariants of singularities that come up in birational geometry are defined in terms of divisorial valuations, or equivalently, in terms of resolutions of singularities. I will describe invariants defined in positive characteristic via the Frobenius morphism. They are related in a subtle, partly conjectural way with the invariants in characteristic zero. I will talk about joint work with Manuel Blickle and Karen Smith regarding the rationality of these invariants.