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

• • Oct 062025

  Zhouli Xu (University of California, Los Angeles)

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  Proof of the existence of $\theta_6$

  The Kervaire invariant problem asks in which dimensions there exists a stably framed manifold of Kervaire invariant one. Hill–Hopkins–Ravenel resolved this problem in all but one dimension: 126.

  In this talk, I will present an overview of the proof that $h_6^2$ survives in the Adams spectral sequence, thereby resolving the final open case of the Kervaire invariant problem. I will discuss new techniques involved, some of which are inspired by motivic homotopy theory. This is joint work with Weinan Lin and Guozhen Wang.

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• • Oct 202025

  Jared Weinstein (Boston University)

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  On the splitting conjecture of Hopkins

  Hopkins' splitting conjecture predicts the structure of a double localization $L_{K(t)} L_{K(h)} \mathbb{S}$ of the sphere spectrum, where $K(h)$ is Morava $K$-theory at a prime $p$ and $0 < t < h$. Perfectoid techniques give powerful evidence for the conjecture while avoiding explicit computation. We show (a) the conjecture is true for $(h,t) = (2,1)$ and $p$ odd, recovering a difficult result of Shimomura and Yabe, and (b) for $h$ general and $t = h-1$, the conjecture is true 'up to perfection.' This is joint work with Lucas Mann, Rin Ray, and Xinyu Zhou.

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• • Oct 272025

  Aaron Landesman (MIT/Harvard)

• • Nov 032025

  Bowen Yang (Harvard University)

• • Nov 172025

  Akhil Mathew (University of Chicago)

• • Dec 012025

  Daniel Spiegel (Harvard University)

• • 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.