Upcoming Talks

In Spring 2025, the UChicago Algebraic Topology Seminar will meet on Tuesdays at 4:00-5:00PM in Eckhart Hall 206 and will be preceded by a pretalk 3:30-4PM (unless otherwise noted).

To receive emails about the seminar, please email Nikolai Konovalov requesting to be subscribed to our mailing list.

• • May 202025

  Mark Behrens (University of Notre Dame)

  A $C_3$-equivariant Snaith construction

  Snaith showed that the periodic complex cobordism spectrum $MUP$ is equivalent to the Bott-localization of the suspension spectrum of $BU$. More generally, Chatham, Hahn, and Yuan showed that periodic forms of the Brown-Peterson spectrum $BP$ can be obtained by localizing the suspension spectra of most Wilson spaces. I will discuss work in progress with Gabe Angelini-Knoll, Eva Belmont, Max Johnson, and Hana Jia Kong, where we study a spectrum $MUP_{\mu_3}$ which we define to be the localization of a $C_3$-equivariant Wilson space. I will explain how the resulting spectrum is related to the $C_p$-spectrum $BP_{\mu_p}$ constructed by Hu, Kriz, Somberg, and Zou, specialized to the case of $p = 3$. Because $MUP_{\mu_3}$ is an $E_{\infty\rho}$-ring spectrum, it has the potential to fulfill the desiderata of the Hill, Hopkins, and Ravenel program to resolve the $3$-primary Kervaire invariant one problem.

• • May 272025

  Shai Keidar (University of Chicago)

  Higher Galois theory

  This talk is 3:45-4:45 and it is in E308.

  Classical Galois theory is a powerful tool for understanding descent for finite field extensions, with the absolute Galois group organizing all such extensions and Kummer theory connecting them to the Picard group.

  In the infinity-categorical setting, one can go further, studying ''higher'' groups and their corresponding Galois extensions. We develop a Galois theory framework tailored for higher semiadditive categories of height $n$, replacing finite groups with $n$-finite groups. We prove the existence of a pro-$n$-finite ''absolute Galois group'' representing Galois extensions, and establish a higher Kummer theory linking these Galois extensions to the higher Brauer groups of the category.

If you have any questions, please contact Toni Annala, Nikolai Konovalov, Akhil Mathew, Tomer Schlank, or Peter May.