Topology Seminar
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
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Cary Malkiewich (Binghamton University)
$\begingroup $Scissors congruence is the study of polytopes, up to the relation of cutting into finitely many pieces and rearranging the pieces. In the 2010s, Zakharevich defined a "higher" version of scissors congruence, where we don't just ask whether two polytopes are scissors congruent, but also how many scissors congruences there are from one polytope to another.
Zakharevich's definition is a form of algebraic K-theory, which is famously difficult to compute, but I will discuss a surprising result that makes the computation of the higher K-groups possible, at least for low-dimensional geometries. In particular, this gives the homology of the group of interval exchange transformations, and a new proof of Szymik and Wahl's theorem that Thompson's group V is acyclic. Much of this talk is based on joint work with Anna-Marie Bohmann, Teena Gerhardt, Mona Merling, and Inna Zakharevich, and also with Alexander Kupers, Ezekiel Lemann, Jeremy Miller, and Robin Sroka.
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Rok Gregoric (Johns Hopkins University)
$\begingroup $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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David Lee (MIT)
$\begingroup $TBA
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J.D. Quigley (University of Virginia)
$\begingroup $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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Andy Senger (Harvard University)
$\begingroup $TBA
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Cameron Krulewski (MIT)
$\begingroup $The seminar will meet at 5:30 PM in 2-135.
TBA
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Melody Chan (Brown University)
$\begingroup $The seminar will meet at 3:30 PM in 2-132.
TBA
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Ishan Levy (University of Copenhagen)
$\begingroup $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.