Department of Mathematics

Speaker: Ettore Aldrovandi
Title: Intersection Theory and Homotopy Types with Algebraic Structure
Affiliation: Florida State University
Date: Wednesday, November 18, 2015
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 from intersection theory to motivate looking at sheafified homotopy types (stacks).

Homotopy types are meant to encode the connectivity information of spaces, and to do so they must be equipped with some kind with algebraic structure, typically like that of a group or a ring, only up to homotopy. I will explain the main ideas informing this kind of "brave new geometry", and illustrate some results of my own about the computation of mapping spaces and the classification issue.

After this journey through homotopy theory, I will return to intersection theory to show how these techniques can be effectively employed to describe codimension two cycles in a smooth scheme and the intersection product of codimension one cycles. (This last part is joint work with N. Ramachandran.)