SPEAKER: Vadim Vologodsky

TITLE: The sheaf of vanishing cycles

ABSTRACT: I will explain the notion in the title. Then, as a first application, I will prove the Local Monodromy Theorem of Grothendieck: the eigenvalues of the monodromy operator acting on the cohomology groups of a family of compact algebraic varieties over a punctured disk are all roots of unity. As another application I will explain a result from a joint work with AJ Stewart on birational invariants of algebraic varieties.