Title: Finite order birational automorphisms of Fano hypersurfaces

Abstract: The birational automorphism group of an algebraic variety is a geometric invariant which exhibits very interesting behavior in families. In this talk, we will explain the specialization homomorphism for finite order birational automorphisms. Building on previous work of Kollar and C-Stapleton, as an application we show that very general n-dimensional hypersurfaces of degree d≥5⌈(n+3)/6⌉ have no finite order birational automorphisms. This is joint work with Lena Ji and David Stapleton.