Behavior of some invariants in characteristic p

Title: Behavior of some invariants in characteristic p

Abstract: There are many numerical invariants of a ring in 
characteristic p measuring its singularity. In this talk, we will 
discuss two classical ones, Hilbert-Kunz multiplicity and the 
F-signature, and a rather recent one, the F-rational signature. We 
will discuss several properties of these invariants, including 
semi-continuity and behavior under smooth extensions.