Summary

The eCHT Equivariant Algebra Reading Seminar is an online reading seminar in Winter 2021. The target audience is graduate students and postdoctoral faculty, although more senior faculty are also welcome.

Equivariant algebra, or algebra with Mackey and Tambara functors, is an increasingly important tool in equivariant stable homotopy theory. This seminar aims to understand equivariant algebra and its applications.

We will begin by understanding some basic objects, such as equivariant cohomology theories, Mackey functors, and Tambara functors. We will then investigate more sophisticated notions, including modules and algebras, ideals and spectra, and cohomology theories for Tambara functors.

A secondary goal of this seminar is to produce a useful collection of lecture notes. There is a lot of literature on equivariant algebra, but there is no central reference for the material. Participants will be asked to contribute detailed notes for their talks which will be made publicly available after the seminar.

A detailed list of references will be made available in an extended abstract/syllabus. The following references serve as a starting point:

• Webb, A guide to Mackey functors
• Strickland, Tambara functors
• Blumberg-Hill, Incomplete Tambara functors

Prerequisites

Participants should have some background in category theory and basic equivariant stable homotopy theory.  Previous exposure to equivariant algebra (e.g. Mackey functors, Tambara functors) is not strictly necessary but could be helpful.

Expectations

Participants in the seminar will:

• Attend weekly online presentations.
• Give at least one presentation.
• Spend approximately one hour per week preparing for each presentation by skimming the material to be presented.
• Participate actively in an online discussion board on Canvas, by posting comments, asking questions, or responding to other comments.
• Contribute to the production of detailed lecture notes.

The work of the seminar will remain private among the participants. We may record presentations, but only for use by other participants. Our discussion board will not be made available to the public.

Presentations can be given with prepared beamer slides, or with hand-written notes on a tablet. See recent eCHT seminar recordings for some examples of both styles.

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 eCHT Equivariant Algebra Reading Seminar is organized by

• J.D. Quigley (Cornell University), jdq27@cornell.edu
• David Mehrle (Cornell University), dfm223@cornell.edu
  
• Sarah Petersen (University of Notre Dame), speter13@nd.edu

Contact any organizer for more information.

Application

Please submit an application form by Sunday January 3 if you are interested in participating.

Schedule

The seminar meets weekly on Tuesdays at 10:00am (eastern time), starting on 19 January and ending on 27 April.