EVENT DETAILS AND ABSTRACT

Title: Nearby cycles over general bases and stratified homotopy type
Speaker: David Treumann
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

Let $S$ be either a Riemann surface or a scheme of dimension one. To a morphism $f:X \to S$, a construction of Milnor and Grothendieck associates a sheaf on each fiber $f^{-1}(s)$ of $f$, called the sheaf of nearby cycles. If $S$ is replaced by a space or scheme of higher dimension (a "general base" in the title), this construction sometimes goes wrong. Deligne proposed a framework -- the "vanishing topos" of $f$ -- for analyzing this behavior. His proposal has been carried out in the complex analytic setting by Le and Sabbah, and much more recently in the etale setting by Orgogozo. There does not yet exist a comparison theorem between the analytic and etale constructions of nearby cycles over general bases. In the talk I will survey the theory and discuss a work in progress toward obtaining such a comparison result.