SoSe 22 Oberseminar: Tempered cohomology and equivariant elliptic cohomology

Time and place: Tuesday 14:15-15:45 in M311 and online


Tempered cohomology is a global equivariant cohomology theory associated with a p-divisible group over an E-infinity-ring, which provides higher-chromatic generalizations of equivariant topological K-theory. It is a unifying framework connecting all of the following concepts: p-divisible groups and formal groups, global equivariant homotopy theory, the Atiyah–Segal completion theorem, and the classical and chromatic character theory of finite groups.

The goal of this seminar is to learn the basics of tempered cohomology following Jacob Lurie’s Elliptic Cohomology III. We will also review some of the theory of spectral elliptic curves (whose associated tempered cohomology is equivariant elliptic cohomology) and Lurie’s construction of the E-infinity-ring of topological modular forms. Some working knowledge of higher category theory and E-infinity-ring spectra will be assumed.

Date Speaker Topic
03.05 Denis Nardin Introduction
10.05 Denis Nardin Spectral algebraic geometry
17.05 Toni Annala Spectral formal groups
24.05 Niklas Kipp Orientations and Quillen formal groups
31.05 Luca Pol Barsotti–Tate groups
07.06 Denis Nardin The construction of elliptic cohomology
14.06 Marco Volpe Orbispaces and equivariant homotopy theory
21.06 Marc Hoyois The tempered cohomology associated to a preorientation
28.06 Massimo Pippi Equivariant K-theory as tempered cohomology
05.07 Luca Pol The Atiyah–Segal comparison map
12.07 Lucy Yang The character map for tempered cohomology
19.07 Marc Hoyois The Atiyah–Segal completion theorem