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

• • Apr 142025

  Rok Gregoric (Johns Hopkins University)

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  Even periodization of spectral stacks

  The seminar will meet at 3:00 PM in 2-449.

  In this talk, I will present work in progress on even periodization. This is an operation on spectral stacks, which roughly approximates them as closely as possible by using only affines corresponding to even periodic ring spectra. It turns out to have close connections to the even filtration of Hahn-Raksit-Wilson, the prismatization stacks of Bhatt-Lurie and Drinfeld, as well as the chromatic affineness results for topological modular forms of Mathew-Meier.

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• • Apr 142025

  David Lee (MIT)

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  On the p-local homotopy type of truncated Brown—Peterson spectra

  It is a result of Adams and Priddy that $BSU$ admits a unique infinite loop space structure after localization at a prime $p$. On the way to proving this statement, they prove that the $p$-localized connective complex $K$-theory spectrum $ku_{(p)}$ is characterized by its $\mathbb F_p$-cohomology as a Steenrod module. I will talk about a generalization of this part to truncated Brown—Peterson spectra $BP\langle n\rangle$ at odd primes, which can be thought of as higher chromatic analogues of the connective complex $K$-theory. In particular, since the $\mathbb F_p$-cohomology depends only on the $p$-completion, a part of this result is that we can recover the $p$-local homotopy type of $BP\langle n\rangle$ from its $p$-completion. Finally, I will describe some applications and open questions, including the status of the problem at $p=2$.

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• • Apr 212025

  J.D. Quigley (University of Virginia)

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  Some applications of the topological modular forms of projective spaces

  Hurewicz homomorphisms allow one to detect nontrivial elements in the stable homotopy groups of spheres by mapping them to the (often simpler) generalized homology groups of spheres. In previous work with Behrens and Mahowald, we computed the image of the 2-local Hurewicz homomorphism for topological modular forms, which allowed us to detect many new infinite families in the stable stems. In this talk, I will explain some recent work with Bhattacharya and Bobkova leveraging these computations, together with computations of the tmf-homology of small projective spaces, to produce additional infinite familes. Time permitting, I will also describe work in progress, building on Bauer’s computation of the tmf-cohomology of the infinite complex projective space, to detect smooth free circle actions on exotic spheres in arbitrarily high dimensions.

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• • Apr 282025

  Andy Senger (Harvard University)

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  TBA

  TBA

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• • Apr 282025

  Cameron Krulewski (MIT)

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  TBA

  The seminar will meet at 5:30 PM in 2-135.

  TBA

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• • May 052025

  Melody Chan (Brown University)

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  TBA

  TBA

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• • May 122025

  Ishan Levy (University of Copenhagen)

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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.