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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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 $We share current work which goes back and forth between geometric and algebraic topology. We start with generalization of Milnor invariants of links, which works beyond where their indeterminacy limits them and extends to links any three-manifold. This generalization arises from analysis of the classical bar construction. (So we are making progress by connecting two pieces of mathematics developed in Fine Hall in the 1950’s.) These ideas also lead to new algorithms to produce all polynomial functions on presented groups. We then share recent work relating cup product to intersection product on geometric cochains through vector field flows. This leads to a conjectural new approach to E-infinity structure on cochains by “resolving partial-definedness” rather than resolving non-commutativity. What unites these projects is a goal of producing homotopy invariants through a combination of tools including geometric cochains, configuration spaces and bar constructions.
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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)
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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)
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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.