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

• • Nov 172025

  Akhil Mathew (University of Chicago)

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  Sheared Witt vectors (after V. Drinfeld, E. Lau, and T. Zink)

  Motivated by Dieudonne theory, V. Drinfeld and E. Lau introduced a 'decompletion' of the ring of Witt vectors W(R) of a derived p-complete ring R such that (R/p)_{red} is perfect, extending a construction of T. Zink. I will explain various characterizations of this decompletion (called the sheared Witt vectors) and some examples. (Joint work in progress with Bhargav Bhatt, Vadim Vologodsky, and Mingjia Zhang.)

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• • Dec 012025

  Daniel Spiegel (Harvard University)

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  A Classifying Space for Phases of Matrix Product States

  Alexei Kitaev has conjectured that there should be a loop spectrum consisting of spaces of gapped invertible quantum spin systems, indexed by spatial dimension d of the lattice. Motivated by Kitaev's conjecture, I will detail a concrete construction of a topological space B consisting of translation invariant injective matrix product states (MPS) of all physical and bond dimensions, which plays the role Kitaev's space in dimension d = 1. Having such a space is a useful tool in the discussion of parametrized phases of MPS; in fact it allows us to define a parametrized phase as a homotopy class of maps into B. The space B is constructed as the quotient of a contractible space E of MPS tensors modulo gauge transformations. The projection map from E to B is a quasifibration, from which we can compute the homotopy groups of the classifying space B by a long exact sequence. In particular, B has the weak homotopy type $K(Z,2) \times K(Z,3)$, shedding light on Kitaev's conjecture in the context of MPS.

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• • Dec 082025

  Ismael Sierra Del Rio (University of Toronto)

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