MA8403 Topics in Algebraic Topology

This year MA8403 will be on equivariant homotopy theory.

NB: For some reason, it may be that you need to sign up with MA8406 instead of MA8403.

Lectures will be held Wednesdays 12:15 - 14:00 and Fridays 8:15 - 10:00 in MA23. If possible, lectures will be recorded and uploaded to Panopto.

Since this is a PhD level course, the course will be pass/fail only. The deliverable (`exam') will be to give a talk of around 30 minutes on a recent(ish) paper in equivariant homotopy theory, or something related to the course. Depending on the number of students/length of the paper, it may be useful to do this in groups of 2 or 3. Here are some suggestions (if you have others, feel free to get in touch). Note that in most cases, there is a specific part of the paper that I have in mind - it's generally not expected that you read and understand the entire paper.

• The spectrum of the equivariant stable homotopy category of a finite group - Balmer, Sanders
• Spectral Mackey functors and equivariant algebraic K-theory (I) - Barwick
• The Equivariant Slice Filtration: a Primer - Hill
• A new formulation of the equivariant slice filtration with applications to C_p-slices - Hill, Yarnall (would go well with the previous talk)
• An Equivariant Tensor Product on Mackey Functors - Hill, Mazur
• Box Product of Cp-Mackey Functors - Loyd
• Nilpotence and descent in equivariant stable homotopy theory - Mathew, Naumann, and Noel
• A structure theorem for RO(C2)-graded Bredon cohomology - Clover May (who is located in office 1202 :) )
• The Structure of Mackey Functors - Thevenaz, Webb.

Here is a preliminary plan, which is likely to change.

I will continually be updated a set of lecture notes from the course. The PDF can be found here, while the GitHub repository is at https://github.com/drewheard/MA8403-Notes/