Speaker: Sven van Nigtevecht，University of Bonn

Inviter: 邹佛灵

Title: Synthetic modular forms

Language: English

Time & Venue: 2026.10.19 16:00-17:00 Zoom Meeting ID: 883 2659 8049 Passcode: 211748

Abstract: Topological modular forms play an essential role in modern homotopy theory, in particular in computations of the homotopy groups of spheres. This requires an understanding of the homotopy groups of tmf. In this talk, I will explain a longstanding circularity in the literature on this computation, and a resolution of it through the use of a synthetic spectrum called Smf (synthetic modular forms). The construction of Smf is part of a larger result that lifts spectral sequences to synthetic spectra, allowing for comparisons to Adams–Novikov spectral sequences as well as a host of computational techniques to be applied. This is joint work with Christian Carrick and Jack Davies.