Bonn Topology Group - Abstracts

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Talk

October 21, 2025
Sven van Nigtevecht (Universität Bonn): Synthetic spectra and synthetic modular forms

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, but a complete proof of this computation has never appeared in the literature. In this talk, I will discuss how the modern theory of synthetic spectra can be used to do this computation. One of the key points is that, while spectral sequences do not form a good category, synthetic spectra have a well-behaved homotopy theory, making them much more flexible. A showcase of this flexibility is our construction of a synthetic spectrum we call Smf, for synthetic modular forms, though other examples abound. This is joint work with Christian Carrick and Jack Davies.

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