Algebra/Topology Seminar by Jay Shah

Algebra/Topology seminar by Jay Shah (MIT)

Title: Parameterized higher category theory

Abstract: In this talk, I will first give an overview of a program, joint with Barwick, Dotto, Glasman, and Nardin, to extend the theory of ∞-categories so as to incorporate and provide common footing for certain constructions arising in a host of examples, ranging from equivariant stable homotopy theory to cyclotomic spectra to the calculus of functors. As I will explain, to do this one must in the first instance develop the ∞-category theory of the (∞,2)-category of Cat_∞-valued presheaves on an "atomic orbital" ∞-category. Delving into the details, I will then explain how Lurie's model categories of marked simplicial sets provide an effective formalism for accomplishing this task.