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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Ben Knudsen (Northeastern University)
$\begingroup $We continue the study of the probabilistic versions of the Lusternik–Schnirelmann category and topological complexity introduced in joint work with Weinberger and independently by Dranishnikov–Jauhari. In the aspherical context, where these invariants are group invariants, there is a universal upper bound in the finite case. We discuss progress toward calculating the exact value, which is equivalent to an interesting problem in equivariant homotopy theory. This talk is based on joint work with Shmuel Weinberger.
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Mirai Ikebuchi (Kyoto University)
$\begingroup $Cohomology of Lawvere theories — small categories with finite products, also called algebraic theories — is studied by Jibladze and Pirashvili. They considered three types of definitions, Quillen, Baues-Wirsching, and Ext cohomologies, and showed that their equivalences. In this talk, we extend their work to small cartesian closed categories. Also, we will briefly see its application to logic and theoretical computer science. As Lawvere theories are categorical formulation of universal algebra, there is a famous correspondence between cartesian closed categories and equational theories on simply typed lambda calculus. So, cohomology of cartesian closed categories is an invariant of such equational theories.
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Dev Sinha (University of Oregon)
$\begingroup $TBA
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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 $TBA
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David Lee (MIT)
$\begingroup $TBA
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J.D. Quigley (University of Virginia)
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Andy Senger (Harvard University)
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Melody Chan (Brown University)
$\begingroup $TBA
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Ishan Levy (University of Copenhagen)
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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.