Kervaire invariant seminar

This is the webpage for the seminar on the Kervaire invariant one problem. Before the summer, we treated some of the historical background on this problem, see here. This semester, the autumn of 2019, we will have weekly meetings where we study the solution to this problem by Mike Hill, Mike Hopkins and Douglas Ravenel.

PhD students from SU or KTH can receive 7.5 ECTS for participating. The syllabus, which includes the requirements for receiving credits, can be found here.

Location: Sal 16, Hus 5, Kräftriket, Department of Mathematics, Stockholm University .

Time slot: Tuesday morning 10:15 AM - 12:00 PM.

Start: October 1, 10:15 AM.

Schedule:

• October 1, Thomas Blom: Introduction (notes).
• October 8, Louis Hainaut: Categories enriched over (Top.,∧); introduction to model categories (notes).
• October 15, Jeroen Hekking: Introduction to (orthogonal) spectra, the smash product on orthogonal spectra (notes).
• October 22, Greg Arone: Equivariant unstable homotopy theory (here are notes that were live TeX'd by Alvin, with some additions by Thomas).
• October 29, Hadrien Espic: Equivariant stable homotopy theory (Orthogonal G-spectra).
• November 5, Thomas Blom: Mackey functors, fixed points and norm construction (notes and exercises on Mackey functors).
• November 12, Asaf Horev: The spectral sequence of a tower; Adams(-Novikov) spectral sequence; Homotopy fixed point spectral sequence.
• November 19, Erik Lindell: Construction of the C₈-spectrum Ωₒ; equivalence of the homotopy fixed points and actual fixed points of Ωₒ.
• November 26, Johan Konter: The detection theorem.
• December 3, Kristian J. Moi: The slice filtration and the slice spectral sequence.
• December 10, Tomas Zeman: The slice tower of MU⁽⁽ᶜ⁸⁾⁾.
• December 17, room 31 (instead of 16), Johan Konter: The gap theorem.
• January 7, Robin Stoll: The periodicity theorem.

References:

• On the nonexistence of elements of Kervaire invariant one, by Hill-Hopkins-Ravenel: Published version, arXiv version.
• Ravenel's homepage contains many references.
• In particular, it contains the book project Equivariant stable homotopy theory and the Kervaire invariant problem, which treats a lot of the foundational background material.
• Notes by Mike Hill from a workshop on the Kervaire invariant that he gave in Israel in 2012: http://math.haifa.ac.il/blanc/work12.html.
• The 2016 MIT Talbot workshop, mentored by Mike Hill and Douglas Ravenel, was about the Hill-Hopkins-Ravenel solution to the Kervaire invariant one problem. The section Talks and notes contains notes on the subjects that we will treat in the seminar.
• Stefan Schwede's notes on (equivariant) orthogonal spectra.
• More to come...