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 272025

  Aaron Landesman (MIT/Harvard)

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  Homological stability for Hurwitz spaces

  Last year in this seminar, I discussed some work with Ishan Levy where we were able to compute the stable homology of Hurwitz spaces associated to dihedral groups, by introducing some ideas coming from higher algebra. Since then, we have been able to generalize our results to compute the stable homology of Hurwitz spaces associated to arbitrary groups. We will start with some background on Malle's conjecture in number theory, which we can prove over function fields by showing the homology of Hurwitz spaces stabilizes. I will then discuss a refinement of Malle's conjecture called Bhargava's conjecture, which we can prove over function fields by computing the stable value of the homology. I will explain some of the key new ideas in these proofs. I will not assume you have been at any of my previous talks.

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• • Nov 032025

  Bowen Yang (Harvard University)

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  Quantum Cellular Automata and Algebraic L-Theory

  Quantum cellular automata (QCAs) are models of reversible quantum dynamics that preserve locality; they can be thought of as quantum analogues of classical cellular automata, but with much richer structure. I will describe a classification of the Clifford subclass of QCAs using methods from algebraic L-theory. The main result identifies the group of Clifford QCAs, up to natural equivalences, with L-theory homology of the underlying space. This gives a conceptual explanation of previously observed periodic patterns in lattice models and extends the picture to more general spaces. I will outline the ideas behind the construction and indicate how the framework connects topology, operator algebras, and quantum information. If time permits, I will also comment on what is known–and unknown–about the general (non-Clifford) case.

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• • 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.