Topology Seminar
Upcoming Talks
In Fall 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.
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Sanath Devalapurkar (UChicago)
Local Tate duality for ring spectra
Tate duality is a form of Poincare duality for the absolute Galois group of a $p$-adic local field $F$, which says that from the perspective of étale cohomology, $\mathrm{Spec}(F)$ behaves like a $2$-manifold. This was refined by Bhatt-Lurie to show that under this duality, the syntomic cohomology of $\mathscr{O}_F$ forms a Lagrangian subspace of $\mathrm{H}^*_{\text{ét}}(F)$. An equicharacteristic generalization was proved by Kato, where it was shown that ''n-local fields'' behave like closed $(n+1)$-manifolds. I will describe some joint work with Jeremy Hahn and John Rognes, where we define the notion of a ''higher local number ring'' and prove a version of Tate duality, which says that higher local number rings of height $n-1$ behave like closed $(n+1)$-manifolds. In particular, I will sketch two key ingredients of our argument, namely duality at the level of $\mathrm{THH}$, and a motivically filtered lift of the transfer map on $\mathrm{THH}$. Both use the theory of finite Hopf algebras over perfect fields.
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Alexander Petrov (Clay/MIT)
If you have any questions, please contact Sanath Devalapurkar, Nikolai Konovalov, Akhil Mathew, Tomer Schlank, or Peter May.