Summary

The eCHT Floer Homotopy Theory Reading Seminar is an online reading seminar in Winter 2022. The target audience is advanced graduate students, postdoctoral researchers, and faculty. More junior graduate students may be accepted if space allows.

Floer homologies are ways of assembling moduli spaces of solutions to certain PDE’s into computable homology-like invariants of certain geometric situations. The broad collection of Floer homologies available have seen extensive application to symplectic geometry and low-dimensional topology. Cohen-Jones-Segal envisioned a far-reaching generalization, interpreting Floer homologies as the homology of certain \textit{Floer spectra}. Various incarnations of Floer spectra have appeared since, and recently there has been a great growth of interest, and potential application, with the construction of Hamiltonian Floer Morava K-theories by Abouzaid-Blumberg.

This seminar will consist of a few blocks, which may be adjusted to fit the interests of participants:

(1) An introduction to Floer spectra, via the Cohen-Jones-Segal paper.

(2) The proof of Furuta’s 10/8 Theorem, using only equivariant K-theory and the Seiberg-Witten equations. This may also include a discussion of the Seiberg-Witten Floer spectrum.

(3) Abouzaid-Blumberg’s Hamiltonian Floer Morava K-theory.

We hope also to shed light on some potential research directions and point to concrete questions in the field.

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 share online workspace.

Students are encouraged to obtain independent study credit from their home universities for their participation in the seminar, but this is not required.

Organizers

The seminar is organized by Matt Stoffregen (Michigan State University) and Alice Hedenlund (Uppsala University). Contact either for more information.

Application

 Please submit the application form to apply. Applications received by January 13 will receive full consideration. 

Schedule

The seminar meets on Tuesdays at 10:30-12:00 (eastern time).