Department of Mathematics

Speaker: Ettore Aldrovandi
Title: Stacks and Homotopy Types: Intersections and Applications
Affiliation: Florida State University
Date: Friday, April 21, 2017
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. I will use some simple ideas and examples, some chosen from intersection theory, to introduce two intimately related ideas: that of a stack and of a homotopy type.

Stacks arise from the desire to parametrize species of mathematical objects, like all triangles in the plane, all quadruples of points on the sphere, "all" algebraic curves of a given genus; homotopy types arise from the desire to encode the connectivity information of spaces. Both kinds are usually equipped with some kind of algebraic structure, typically like that of a group or a ring, only "up to homotopy".

After the introductory examples, I will illustrate some aspects of this "brave new algebra" and present some recent applications, results, and some work in progress, in intersection theory, generalized differential operators, and K-Theory (in collaboration with with N. Ramachandran, U. Bruzzo, and some of my students).