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Topology Seminar

The Topology Seminar has talks on a variety of topics in topology, including algebraic geometry, applications of higher category theory to geometry and mathematical physics, chromatic homotopy theory, continuum theory, deformation theory, homotopical algebra, Nielsen fixed-point theory, simplicial sets, span theory, and topological groups.
For more information contact Daniel Davis.

Fall 2017

For the Fall 2017 semester we will meet at 1:00 on Fridays in 208 Maxim Doucet Hall.

  • 8 September 2017
    An introduction to the Goerss-Hopkins Linearization Hypothesis and a connection to continuous G-spectra.
    Daniel Davis
  • 15 September 2017
    More about the Goerss-Hopkins Linearization Hypothesis and a connection to continuous G-spectra.
    Daniel Davis
  • 22 September 2017
    The Goerss-Hopkins Linearization Hypothesis and continuous G-spectra, part 3.
    Daniel Davis
  • 29 September 2017
    The Goerss-Hopkins Linearization Hypothesis and continuous G-spectra, part 4.
    Daniel Davis
  • 13 October 2017
    The Goerss-Hopkins Linearization Hypothesis and continuous G-spectra, part 5.
    Daniel Davis
  • 20 October 2017
    Finite-type invariants of knots, links, and string links
    Robin Koytcheff
    Abstract: Finite-type knot invariants (a.k.a. Vassiliev invariants) are an important class of invariants in that they conjecturally approximate all knot invariants and hence separate knots. They may also be defined for (closed) links and string links, and they are known to separate string links up to link homotopy. In other words, they are a complete invariant of string links where each component may pass through itself. This parallels (and is related to) a story about the kappa invariant, which conjecturally separates closed links up to link homotopy. In joint work with F. Cohen, Komendarczyk, and Shonkwiler, we showed that the kappa invariant separates string links up to link homotopy. In this talk, we will focus on the elementary, purely combinatorial description of finite-type invariants.
  • 27 October 2017
    Homotopy string links, configuration spaces, and the kappa invariant
    Robin Koytcheff
    Abstract: A link is an embedding of disjoint circles in space. A link homotopy is a path between two links where distinct components may not pass through each other, but where a component may pass through itself. In the 1990s, Koschorke conjectured that link homotopy classes of n-component links are distinguished by the kappa invariant. This invariant is essentially the map that a link induces on configuration spaces of n points. In joint work with F. Cohen, Komendarczyk, and Shonkwiler, we proved an analogue of this conjecture for string links. A key ingredient is a multiplication on maps of configuration spaces, akin to concatenation of loops in a space. This approach is related to recent joint work with Budney, Conant, and Sinha on finite-type knot invariants and the Taylor tower for the space of knots.
  • 17 November 2017
    The Simplicial Model Category Structure on Symmetric Spectra
    Thomas Credeur

Spring 2017

For the Spring 2017 semester we will meet at 1:00 on Fridays in 208 Maxim Doucet Hall.

  • 27 January 2017
    Genuine equivariant operads
    Luis Pereira
    University of Virginia
     
    Abstract: A fundamental result in equivariant homotopy theory due to Elmendorf states that the homotopy theory of $G$-spaces, with w.e.s measured on all fixed points, is Quillen equivalent to the homotopy theory of $G$-coefficient systems in spaces, with w.e.s measured at each level of the system. Furthermore, Elmendorf's result is rather robust: suitable analogue results can be shown to hold for, among others, the categories of (topological) categories and operads. However, it has been known for some time that in the $G$-operad case such a result does not capture the "correct" notion of weak equivalence, a fact made particularly clear in recent work of Blumberg and Hill discussing a whole lattice of "commutative operads with only some norms" that are not distinguished at all by the notion of w.e. suggested above. In this talk I will talk about one piece of a current joint project with Peter Bonventre which aims at providing a more diagrammatic understanding of Blumberg and Hill's work using a notion of $G$-trees, which are a somewhat subtle generalization of the trees of Cisinski-Moerdijk-Weiss. More specifically, I will describe a new algebraic structure, which we dub a "genuine equivariant operad", which naturally arises from the study of $G$-trees and which we conjecture to be the analogue of coefficient systems in the "correct" analogue of Elmendorf's theorem for $G$-operads.
  • 3 February 2017
    No meeting
  • 10 February 2017
    No meeting

Fall 2016

For the Fall 2016 semester we will meet at 1:00 on Fridays in 208 Maxim Doucet Hall.

  • 16 September 2016
    An introduction to infinity-categories and the example of small categories.
    Daniel Davis
  • 23 September 2016
    Infinity-categories: more on the example of small categories and infinity-categorical versions of basic category-theoretic notions.
    Daniel Davis
  • 30 September 2016
    Some examples of infinity-categorical concepts that build on category-theoretic notions.
    Daniel Davis
  • 14 October 2016
    The notions of join and overcategory in the setting of infinity-categories.
    Daniel Davis
  • 21 October 2016
    Simplicial nerves and the homotopy category of an infinity-category.
    Daniel Davis
  • 28 October 2016
    The homotopy category of an infinity-category and a nicer formulation of it.
    Daniel Davis
  • 4 November 2016
    Given an \infty-category C, there is an isomorphism h(C) \to \pi(C) of categories.
    Daniel Davis
  • 11 November 2016
    Given an \infty-category C, more on the category \pi(C), and equivalences in C.
    Daniel Davis

Topology Seminar Archive