Even periodizationMPIM

by Rok Gregoric (MPIM)

Tuesday Oct 20, 2026, 11:00 AM → 12:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Abstract homotopy theory seminar

A commutative ring spectrum is called even periodic if its homotopy groups vanish in odd degrees and are (at least locally) pairwise isomorphic in even degrees. Such rings are quite far from the usual setting of algebraic geometry, based on static rings concentrated in a single homotopy degree, or even the standard setup of derived geometry, based on connective rings. Yet algebro-geometric spaces that are locally of this form abound in applications to homotopy theory, especially chromatic theory. In this talk, we will discuss the operation of even periodization, which universally approximates a derived stack with an even periodic one, and discuss some applications this unassuming construction has to the Hahn-Raksit-Wilson even filtration, prismatic cohomology, and more.