Topology Seminar

Chromatic analogues of the Hopkins-Mahowald theorem

Sanath Devalapurkar, Harvard University

Friday, March 12th, 2021
2:00 PM - 3:00 PM
Zoom ID 677 596 7436

https://rochester.zoom.us/j/6775967436

An important theorem of Hopkins and Mahowald shows that the Eilenberg-Maclane spectrum HF_2 can be obtained as the Thom spectrum of a specific bundle over Loops^2 S^3. In this talk, I will discuss a generalization of this result to Brown-Peterson spectra BP, connective real K-theory bo, and connective tmf. This generalization relies on some deep results in unstable homotopy theory relating to the Cohen-Moore-Neisendorfer theorem, as well as a conjecture about the E_3-centers of certain E_2-rings which feature in the proof of the nilpotence theorem. This connection hints at a deep relationship between chromatic and unstable homotopy theory, and I hope to state some interesting questions along these lines.

Event contact: steven dot amelotte at rochester dot edu