Upcoming Talks

The seminar will meet at 4:30 on Monday in 2-131 unless otherwise noted.

Click here to add this seminar to your google calendar. If you use a different calendar program, the ics file for this seminar is here:
http://math.mit.edu/topology/topology_seminar.ics

• • Nov 042024

  Shai Keidar (University of Chicago)

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  Higher Galois theory in chromatic homotopy theory

  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, extending previous work by Akhil Mathew, and establish a higher Kummer theory linking these Galois extensions to the higher Brauer groups of the category. Focusing on the telescopic category, we construct new elements in the Picard and Brauer groups and relate them to Galois extensions of the T(n)-local sphere.

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• • Nov 182024

  Aaron Landesman (Harvard University)

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  The stable homology of dihedral group Hurwitz spaces and the Cohen-Lenstra heuristics

  Hurwitz spaces are moduli spaces for certain branched covers of the disc. In a 2016 Annals paper, Ellenberg-Venkatesh-Westerland showed that the homology of Hurwitz spaces associated to dihedral groups stabilize as one increases the number of branch points. However, their work left open the question of what the homology stabilizes to. In joint work with Ishan Levy, we compute the stable value of these homology groups. As a consequence, we are able to verify many predictions of the Cohen-Lenstra heuristics in number theory.

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• • Nov 252024

  Allen Yuan (Northwestern University)

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