Zeta functions and decomposition spaces

Abstract: Zeta functions show up everywhere in math these days. While some recent work has brought homotopical methods into the theory of zeta functions, there is in fact a lesser-known zeta function that is native to homotopy theory. Namely, every suitably finite decomposition space (aka 2-Segal space) admits an abstract zeta function as an element of its incidence algebra. In this talk, I will show how many 'classical' zeta functions from number theory and algebraic geometry can be realized in this homotopical framework, and outline some preliminary work in progress with Julie Bergner and Matt Feller towards a motivic version of the above story.

The discussion for Andrew Kobin’s talk is taking place not in zoom-chat, but at tinyurl.com/2020-09-11-ak (and will be deleted after 3-7 days).