Topology Seminar
Upcoming Talks
In Winter 2026, the UChicago Algebraic Topology Seminar will meet on Tuesdays at 4:00-5:00PM in Eckhart Hall 202 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.
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Alexander Waugh (University of Washington)
Equivariant Homology Operations
Motivated by Serre's computation of the cohomology of Eilenberg-Maclane spaces using Steenrod operations, Araki and Kudo developed operations on $\mathrm{mod}\;2$ homology of ''nice'' spaces with the goal of studying the homology of $n$-fold loop spaces. Dyer and Lashof later developed odd primary versions of these operations and carried out further computations related to the homology of iterated loop spaces. These Araki-Kudo-Dyer-Lashof operations were later used by P. May and F. Cohen to describe the homology of iterated loop spaces and free $\mathbb{E}_n$-algebras in spaces; a computation which is analogous to Serre's cohomological computations.
In this talk, I will describe a theoretical framework for constructing $G$-equivariant analogs of these operations which act on the $R$-homology of ''nice'' $G$-spaces and $G$-spectra, where $R$ is a $G$-equivariant ring spectrum. This is a generalization of previous joint work with Prasit Bhattacharya, Foling Zou, and Mingcong Zeng constructing equivariant Steenrod operations by describing certain sequences in the homology of equivariant classifying spaces. This framework is joint work with Prasit Bhattacharya. When $R$ is the Eilenberg-Maclane spectrum associated to the constant $\mathbb{F}_p$ Tambara functor, I will outline a new method of constructing such sequences which generalize and simplify computations appearing in joint work with Bhattacharya, Zou, and Zeng. Time permitting, I will discuss how this new perspective gives insight into properties of these operations such as Cartan formulas and Adem relations.
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Akira Tominaga (Johns Hopkins University)
If you have any questions, please contact Sanath Devalapurkar, Nikolai Konovalov, Akhil Mathew, Tomer Schlank, or Peter May.