We are an informal pedagogical seminar concerning algebraic topology and homotopy theory, localized at Harvard and MIT. For Fall 2025, talks will proceed on Thursdays at 1:30 - 2:30 pm ET, located in SC 309a.

This seminar is organized by Thomas Brazelton and Logan Hyslop, who you should email with questions.

References:

• Our main reference is the book The norm residue theorem in motivic cohomology by Haesemeyer and Weibel [HW19].

• • Sep 11 2025

  An introduction to Bloch-Kato and the Milnor conjectures.

  Thomas Brazelton

  Abstract: We will give an overview of ideas for the semester.

  References:

  • Intro to [HW19]
• • Sep 18 2025

  Milnor $K$-theory and étale cohomology

  Rosie Shen

  Abstract: tbd

  References:

  • tbd
• • Sep 25 2025

  The transfer argument

  Logan Hyslop

  Abstract: tbd

  References:

  • [HW19], Chapter 1
• • Oct 2 2025

  Motivic complexes

  Tyler Lane

  Abstract: tbd

• • Oct 9 2025

  Hilbert 90$(n)$ and Bloch-Lichtenbaum

  Thomas Brazelton

  Abstract: tbd

• • Oct 16 2025

  Norm varieties, Rost varieties, and Rost motives

  Matt Broe

  Abstract: tbd

• • Oct 23 2025

  Equivariant motivic cohomology

  tbd

  Abstract: tbd

• • Oct 30 2025

  Motivic cohomology operations

  Jonathan Buchanan

  Abstract: tbd

• • Nov 6 2025

  Rost varieties exist

  Isabel Longbottom

  Abstract: tbd

• • Nov 13 2025

  Rost motives exist

  Jeremy Hahn

  Abstract: tbd

• • Nov 20 2025

  Tying up the proof

  tbd

  Abstract: tbd

• • Nov 27 2025

  🦃 Thanksgiving 🦃

  (no talk)
• • Dec 4 2025

  Application: Quillen-Lichtenbaum

  Keita Allen

  Abstract: tbd

• • Dec 11 2025

  Application: $K(\mathbb{Z})$

  Dhilan Lahoti

  Abstract: tbd