Summary

The topological modular forms spectrum tmf is a connective commutative ring spectrum that serves as an approximation to the sphere spectrum. Its Adams spectral sequence can be computed completely, i.e., in finitely many steps. The structure of this Adams spectral sequence gives a lot of information about the structure of the Adams spectral sequence for the sphere spectrum, and therefore on the structure of the stable homotopy groups of spheres.

The goal of the seminar is to study the computation of the Adams spectral sequence for tmf, following the detailed presentation in the recently published book

MR4284897. Bruner, Robert R.; Rognes, John. The Adams spectral sequence for topological modular forms. Mathematical Surveys and Monographs, 253. American Mathematical Society, Providence, RI, 2021. xix+690 pp. ISBN: 978-1-4704-5674-0

Here is a draft syllabus, subject to change.

Participant expectations

Participants will take turns giving presentations. The seminar organizers will make sure that presenters have written source material upon which to base their presentations. Participants are expected to attend regularly.

Participants are encouraged to skim the source material being presented each week. They are also encouraged to participate in the private shared online workspace.

As a general rule, students are expected to obtain 1-2 independent study credits from their home universities for their participation in the seminar. This requirement is waived on an individual basis for students whose home universities do not have formal independent study opportunities.

Organizers

The seminar is organized by Robert Bruner (Wayne State University), John Rognes (University of Oslo), and Dan Isaksen (Wayne State University). Contact any of the three for more information.

Application

Please submit the application form to apply. Applications received by December 7 will receive full consideration.

Schedule

The seminar meets regularly at 11:00am Eastern time on Tuesdays, starting January 10 and ending April 25.