https://rochester.zoom.us/j/6775967436

The recently developed theory of decomposition spaces, also known as 2-Segal spaces, provides a homotopical setting for the study of various combinatorial problems, via a generalization of the incidence algebra of a poset. The incidence algebra point-of-view applied to classical zeta functions arising in algebra and number theory yields a pleasant way to construct Möbius functions, prove multiplicative identities, and produce generating functions. After surveying some of these constructions, we will describe work in progress with Andrew Kobin (UCSC) which aims to use and extend the techniques of “homotopy linear algebra” as well as recent work of Campbell, Zakharevich, and others on the K-theory of varieties to study Kapranov’s motivic zeta function and the incidence algebras arising from decomposition spaces.