Where:

507 Mathematics

When:

Fridays 9:30am-10:30am (unless otherwise noted)

Date Speaker (affiliation) Title & Abstract
September 12 Speaker: TBA
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Abstract:

September 19 Ningchuan Zhang (Indiana University Bloomington)
Profinite transfers in K(n)-local homotopy theory

Abstract: After K(1)-localization, the classical J-homomorphism can be interpreted as a profinite transfer map. More precisely, it is a transfer map $\Sigma^{-1}KO^\wedge_2 \to S_{K(1)}$ from the $C_2$-homotopy fixed points (with a twist) to the $\mathbb{Z}_2^\times$-homotopy fixed points of the 2-complete complex topological K-theory. In joint work in progress with Guchuan Li, we extend this idea to define and study profinite transfers between homotopy fixed points of the Morava E-theory by closed subgroups of the Morava stabilizer group.

We introduce two definitions of the profinite transfer maps. One ad hoc definition is as duals to the profinite restriction maps in the appropriate category. At large primes, we show that the image of the transfer map $\Sigma^{-n^2}E_n \to S_{K(n)}$ on homotopy groups is the HFPSS filtration n^2-line. A second definition of the profinite transfer maps is based on the 6-functor formalism for smooth representations of p-adic Lie groups by Heyer—Mann. We prove that the ad hoc and the 6-functor definitions are equivalent.

September 26 Speaker: TBA
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October 3 Ishan Levy (Institute of Advanced Study)
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October 10 Speaker TBA
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October 17 at 2pm in 407 Ulrike Tillmann (Oxford University)
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October 24 Speaker TBA
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October 31 Speaker TBA
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November 7 Speaker TBA
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November 14 Samuel Munoz Echaniz (MIT)
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November 21 Mona Merling (University of Pennsylvania)
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November 28 No seminar
December 5 Emily Riehl (Johns Hopkins University)
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Past seminars