Floor Homotopy Theory

Abstract: One perspective on homotopy theory is that it is an enhanced version of arithmetic which remembers combinatorics and symmetry. I will demonstrate this philosophy concretely in the case of the floor and ceiling functions from arithmetic, by explaining several situations where these appear: K-theory of truncated polynomial algebras; Legendre's formula and its q-analogue; hyper-representation-graded TR; and equivariant homotopy theory. To understand how these examples are related, I will show how to construct a Tambara functor out of a prism, and discuss a conjectural theory of G-crystalline/G-de Rham cohomology generalizing q-crystalline cohomology and the q-de Rham complex.

algebraic topology

Audience: researchers in the topic

MIT topology seminar

Series comments: We meet at varying times on Monday. Click here to join the zoom meeting . The Zoom meeting room number is 132-540-375.

The mailing list for this seminar is the MIT topology google group. Email Mike Hopkins if you want to join the list.