Topology Seminar
Upcoming Talks
In Fall 2026, the UChicago Algebraic Topology Seminar will meet on Tuesdays at 3:50-4:50PM in Eckhart Hall 206 and will be preceded by a pretalk 3:20-3:50PM (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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Jiacheng Liang (Johns Hopkins University)
Dualizable Additive Categories
Dualizable stable categories have recently emerged as a useful enlargement of compactly generated stable categories, particularly in algebraic $K$-theory and analytic geometry. In this talk, I will discuss a connective analogue: dualizable additive categories.
I will explain how these categories can be described in terms of almost mathematics and how they can be reconstructed from their flat objects. For a connective adic $E_\infty$-ring $R$, we show that the category $\mathrm{Nuc}(R)_{\geq 0}$ is the additive rigidification of the category of connective complete $R$-modules. In particular, this gives a conceptual categorical characterization of connective nuclear modules and applies to examples such as $\mathrm{Nuc}(\mathbb{Q}_p)_{\geq 0}$. Finally, I will introduce the stable category of prestable motives. Its unit corepresents nonconnective algebraic $K$-theory, providing a connective analogue of the theory of noncommutative motives for stable categories.
This is joint work with Ishan Levy and Vladimir Sosnilo.
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Arpon Raksit (Northwestern University)
If you have any questions, please contact Nikolai Konovalov, Kiran Luecke, Kirill Magidson, Akhil Mathew, Shauly Ragimov, or Peter May.