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 which connects all of the following concepts: p-divisible groups and formal groups, global equivariant homotopy theory, the Atiyah-Segal completion theorem, the classical and chromatic character theory of finite groups.

The goal of this seminar is to learn the basics of tempered cohomology following 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.

• Registration for course work/examination/ECTS: FlexNow

• Presentation: Giving a seminar talk of roughly 90 minutes

• Detailed written report of the seminar talk