Zygotop seminar

We are an informal pedagogical seminar concerning algebraic topology and homotopy theory, localized at Harvard and MIT. Unless otherwise specified, talks will proceed on Wednesdays at 4:30pm ET, located in SC 412, and following a topic chosen by the speaker, organized according to these principles.

This seminar is organized by Keita Allen, who you should email with questions or to be added to the signal group chat. Click here to add this seminar to your google calendar.

• • May 7 2025

  The Adams-Novikov spectral sequence in equivariant and motivic homotopy theory

  Keita Allen

  The Adams-Novikov spectral sequence is a way of resolving stable homotopy by complex cobordism, and provides a powerful tool for understanding topology. In his 1979 work, Bousfield provided us with a renewed understanding of this spectral sequence, connecting it to a notion of ``nilpotence” in the category of spectra, which in particular told us the convergence of the Adams-Novikov spectral sequence is the same thing as saying that the sphere is ``nilpotent-complete” with respect to complex cobordism.

  In my talk, I will give a review of the relationship between the Adams spectral sequence and nilpotence, and give an overview of how one proves the convergence of the Adams-Novikov spectral sequence. Time permitting, I will then discuss to what extent this can be generalized to motivic and equivariant homotopy theory. This talk may discuss joint work with Lucas Piessevaux, and an unpublished result of William Balderrama and Markus Hausmann.

  References:

  • The localization of spectra with respect to homology by Bousfield.
  • Localizations and completions of stable \(\infty\)-categories by Mantovani.