Topology Seminar: Miniseries on topological modular forms and synthetic spectra

MPI f. Mathematik (2026) Topology Seminar: Miniseries on topological modular forms and synthetic spectra. [Teaching Resource] (Unpublished)

	Video (20260126 Nigtevecht - From topological to synthetic modular forms) miniseries_nigtevecht_20260126.mp4 - Presentation Download (494MB)
	Video (20260202 Carrick - Techniques in filtered and synthetic homotopy theory) miniseries_carrick_20260202.mp4 - Presentation Download (478MB)
Preview	Slideshow (20260202 Carrick - Slides) 20260202_Carrick_SmfTalk-6.pdf - Presentation Download (1MB) | Preview
	Video (20260209 Davies - The actual computation) miniseries_davies_20260209.mp4 Download (497MB)
Preview	Slideshow (20260209 Davies - Slides) 20260209_Descent_SS_for_Tmf.pdf Download (15MB) | Preview

Abstract

Topological modular forms (tmf) have long played a big role in modern homotopy theory, with applications ranging from studying bordism, to being a key part of the computation of stable homotopy groups of spheres. However, a complete computation of its homotopy groups has never appeared in the literature.

In this mini-series, we will describe our approach to this computation using modern techniques in synthetic spectra and introducing a synthetic spectrum we call Synthetic modular forms (Smf). In the first talk for a general audience, we will introduce tmf and Smf as well as give an outline of how synthetic spectra naturally appear in our work. In the second talk, a series of generic tools from synthetic spectra will be discussed, giving us general tricks and techniques to compute with these objects. In the final talk, a detailed computation of the spectral sequence associated to Smf, also called the descent spectral sequence, giving a complete calculation of the homotopy groups of tmf.

Item Type:	Teaching Resource
Subjects:	3 Geometry and topology > 55-XX Algebraic topology
Depositing User:	This Admin
Date Deposited:	11 Feb 2026 13:53
Last Modified:	12 Feb 2026 06:50
URI:	https://archive.mpim-bonn.mpg.de/id/eprint/5220

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