Student Homotopy Theory Seminar

In this talk we will investigate what would happen if we were to replace sets by spaces at the very foundations of mathematics. In particular, we will focus on what consequences this would have for algebra, if we were to do such a bold operation. We will begin by discussing fibered categories, one of Grothendieck's greatest insights into homotopy theory, and its further development by Jacob Lurie to the setting of higher categories. We will then proceed to use this tool to categorify what we think "doing algebra" is, and to investigate what would happen with abelian groups if sets were to be replaced by spaces. Speaker(s): Attilio Castano (University of Michigan)