Summary

The eCHT Kervaire invariant one seminar is an online reading seminar in Fall 2020. The target audience is postdoctoral, tenure-track, and tenured faculty, although graduate students are also welcome. The similarly structured eCHT motives reading seminar was held in Winter 2020.

The goal is to understand the solution to the Kervaire invariant one problem. We will study the geometric origins of the problem, its stable homotopy theoretic interpretation, and how methods from equivariant stable homotopy theory can be used to solve it. Topics will include the various formulations of the Kervaire invariant one problem, Real bordism, slice spectral sequences, and the Reduction, Gap, Periodicity, and Detection Theorems.  We may also explore connections between equivariant stable homotopy theory and chromatic homotopy theory.

We will follow carefully chosen written material. We will favor deeper understanding over rushing through a larger body of material.

Participants are expected to have some familiarity with stable homotopy theory including the language and basic properties of spectra; some equivariant homotopy theory including Mackey functors; category theory; and spectral sequences.

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 online discussion boards on Canvas by posting comments, asking questions, or responding to other comments.

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.

Organizers

The eCHT motives seminar is organized by Prasit Bhattacharya (University of Notre Dame) and Dominic Culver (Max-Planck-Institut). Contact either organizer for more information.

Application

Please submit an application form by Wednesday September 2 if you are interested in participating.

Schedule

The seminar meets on Mondays at 12:00pm Eastern time, starting September 14 and ending December 14.