Summary

The eCHT Equivariant Homotopy Theory Seminar is an online reading seminar in Fall 2021. The target audience is graduate students in their first three years of doctoral studies, although older graduate students may be accepted if space allows.

The goal of this seminar is to introduce participants to equivariant homotopy theory, the study of topological spaces with group actions up to equivariant weak homotopy equivalence. The seminar will cover many classical topics, including notable examples of equivariance in algebra and topology, equivariant cohomology theories, applications, and equivariant stable homotopy theory.

Participants are expected to have taken first-year graduate courses in abstract algebra and algebraic topology.

Student Expectations

Students will take turns giving presentations on the contents of textbooks and research papers. The main reference is Equivariant homotopy and cohomology theory (May et al, 1996). Students are expected to attend all presentations.

Over the course of the semester, each student will give an hour-long presentation via Zoom. The presentation can be made using Beamer slides or screen capture software. For example, see recordings of recent eCHT presentations.

Students must skim the source material being presented each week and post a response (at least one paragraph) in the private seminar workspace prior to that week’s talk. These responses can include comments and questions related to the material, as well as how the paper fits into their broader mathematical knowledge. The shared online workspace will also serve as a forum where students can ask questions as they prepare for their presentations.

Each week’s speaker will also prepare a problem set expanding on their presentation. Students are expected to attend a weekly problem session (led by the speaker) where they will work together on the problem set.

Students are encouraged to obtain independent study credit from their home universities for their participation in the eCHT Equivariant Homotopy Theory Seminar, but this is not required.

Organizers

The seminar is run by J.D. Quigley (Cornell University) and Hana Jia Kong (Institute for Advanced Study). Contact either of us for more information.

Application

 Please submit the application form to apply. Applications received by August 25 will receive full consideration. 

Schedule

There will be an organizing meeting on Wednesday, Sept 1st. After that, the seminar meets regularly at 1 pm Eastern on Wednesday for talks and 1 pm Eastern Thursday for problem sessions, starting September 8th, and ending December 9th.