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

• • Sep 152025

  Samuel Muñoz Echániz (MIT)

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  A Weiss–Williams theorem for embedding spaces and an application to diffeomorphisms of solid tori

  There is a programme, largely developed by Weiss and Williams, that aims to understand the homotopy type of the diffeomorphism group of a compact, high-dimensional manifold $M$ in terms of Waldhausen's algebraic $K$-theory of $M$. In this talk, I will give a brief overview of this programme and present an analogue for spaces of embeddings (of compact manifolds $P$ into $M$, say). The main difference with the original programme is that the algebraic $K$-theory of $M$ is replaced by the \emph{relative} algebraic $K$-theory of the pair $(M, M \setminus P)$, which, in many cases, coincides with the relative topological cyclic homology of such a pair—a far more computable invariant. As an application, I will report on ongoing joint work with João Lobo Fernandes computing rational homotopy groups of the diffeomorphism group of solid tori $S^1 \times D^n$, $n>4$. This follows a strategy of Bustamante–Randal-Williams and extends computations of Budney–Gabai and Watanabe in high dimensions.

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• • Sep 222025

  Mark Behrens (Notre Dame)

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  A $C_3$-equivariant Snaith construction

  Snaith showed that the periodic complex cobordism spectrum $\mathrm{MUP}$ can be obtained by localizing the suspension spectrum of $BU$ with respect to the generator of $\pi_2$. Chatham, Hahn, and Yuan proved analogs of this theorem where $BU$ is replaced by a general Wilson space. We consider the localization of the equivariant suspension spectrum of a $C_3$-equivariant Wilson space. I will describe work in progress which compares this spectrum to the spectrum $BP_{\mu_3}$ constructed by Hu, Kriz, Somberg, and Zou. We will revisit their construction and flesh out some details. This represents joint work with Gabe Angelini–Knoll, Eva Belmont, Max Johnson, and Hana Jia Kong.

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• • Sep 292025

  Rok Gregoric (Johns Hopkins University)

• • Oct 062025

  Zhouli Xu (University of California, Los Angeles)

• • Oct 202025

  Jared Weinstein (Boston University)

• • Nov 172025

  Akhil Mathew (University of Chicago)

• • Dec 082025

  Ismael Sierra Del Rio (University of Toronto)

Email Jeremy Hahn 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.