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.

algebraic geometrycategory theorynumber theory

Audience: researchers in the topic

( video )

Comments: 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).

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Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

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