Techniques in filtered and synthetic homotopy theoryMPIM

by Christian Carrick (Universität Bonn)

Monday Feb 2, 2026, 2:00 PM → 3:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPIM Topology Seminar: Miniseries on topological modular forms and synthetic spectra

In this talk, we will survey a broad toolkit of techniques in filtered and synthetic homotopy theory that facilitate spectral sequence computations. There are many such techniques, and we will focus on the ones used crucially in our computation of the descent spectral sequence (DSS) of Tmf. We refine the descent spectral sequence to an E_infty-algebra in MU-synthetic spectra, and this endows the DSS with structure ranging from generalized forms of the Leibniz rule to temporary Toda brackets. We survey these tools from an example-based point of view and set ourselves up for the page-by-page computation of the DSS in the final talk.