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

• • Feb 032025

  Søren Galatius (Columbia University)

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  Hopf algebra spectral sequences related to $K(\mathbb{Z})$ and the Grothendieck–Teichmüller group.

  The general linear group of the integers acts on the symmetric space $GL_n(\mathbb{R})/O(n)$, and the orbit space $X_n$ can be regarded as a "moduli space of real tori". The compactly supported cohomology of these spaces forms the $E_1$ page of a spectral sequence converging to the cohomology of $BK(\mathbb{Z})$, the one-fold delooping of the algebraic $K$-theory space. I will sketch how to construct a Hopf algebra structure on this spectral sequence, and how it maps to another spectral sequence of Hopf algebras, a version of the Connes–Kreimer Hopf algebra. In recent joint work with Brown, Chan, and Payne (2405.11528), we use this map of Hopf algebras to deduce lower bounds for the compactly supported cohomology of $X_n$ and of $\mathcal{A}_n$, the moduli space of principally polarized abelian varieties.

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• • Feb 102025

  Ben Spitz (University of Virginia)

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  The Tambara Affine Line

  In equivariant stable homotopy theory, objects called "Tambara functors" play the role of commutative rings. Tambara functors are abstract algebraic objects: they consist of sets with certain operations satisfying certain axioms; however, the theory of Tambara functors is much less developed than the theory of commutative rings, in part because it is not clear exactly how to define the "Tambara analogs" of many classical notions. Nonetheless, we expect that Tambara functors admit a theory of commutative algebra and algebraic geometry, akin to the story for ordinary commutative rings. In this talk, I will discuss recent progress in developing such a theory for Tambara functors – in particular, we prove a version of the going-up theorem, which allows for the first computation of the "affine line" in Tambara algebraic geometry. This is joint work with David Chan, David Mehrle, J.D. Quigley, and Danika Van Niel.

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• • Feb 242025

  Ben Knudsen (Northeastern University)

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  TBA

  TBA

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• • Mar 032025

  Mirai Ikebuchi (Kyoto University)

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  TBA

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• • Mar 312025

  Cary Malkiewich (Binghamton University)

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  TBA

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• • Apr 212025

  J.D. Quigley (University of Virginia)

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  TBA

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• • Apr 282025

  Andy Senger (Harvard University)

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  TBA

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• • May 052025

  Melody Chan (Brown University)

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  TBA

  TBA

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Email Haynes Miller or Keita Allen for inquiries about the seminar.

The mailing list for this seminar is the MIT topology google group.
Email Mike Hopkins if you want to join the list.