##### Department of Mathematics,

University of California San Diego

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### Math 209: Number Theory Seminar

## Andrew Kobin

#### Emory

## Categorifying zeta and L-functions

##### Abstract:

Zeta and L-functions are ubiquitous in modern number theory. While some work in the past 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 in number theory and algebraic geometry can be realized in this homotopical framework. I will also discuss work in progress towards a categorification of motivic zeta and L-functions.

### May 18, 2023

### 2:00 PM

APM 6402 and Zoom; see https://www.math.ucsd.edu/

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