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 fixedpoint 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 GoerssHopkins Linearization Hypothesis and a connection to continuous Gspectra.
Daniel Davis 
15 September 2017
More about the GoerssHopkins Linearization Hypothesis and a connection to continuous Gspectra.
Daniel Davis 
22 September 2017
The GoerssHopkins Linearization Hypothesis and continuous Gspectra, part 3.
Daniel Davis 
29 September 2017
The GoerssHopkins Linearization Hypothesis and continuous Gspectra, part 4.
Daniel Davis 
13 October 2017
The GoerssHopkins Linearization Hypothesis and continuous Gspectra, part 5.
Daniel Davis 
20 October 2017
Finitetype invariants of knots, links, and string links
Robin Koytcheff
Abstract: Finitetype 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 finitetype 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 ncomponent 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 finitetype 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 CisinskiMoerdijkWeiss. 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 infinitycategories and the example of small categories.
Daniel Davis 
23 September 2016
Infinitycategories: more on the example of small categories and infinitycategorical versions of basic categorytheoretic notions.
Daniel Davis 
30 September 2016
Some examples of infinitycategorical concepts that build on categorytheoretic notions.
Daniel Davis 
14 October 2016
The notions of join and overcategory in the setting of infinitycategories.
Daniel Davis 
21 October 2016
Simplicial nerves and the homotopy category of an infinitycategory.
Daniel Davis 
28 October 2016
The homotopy category of an infinitycategory and a nicer formulation of it.
Daniel Davis 
4 November 2016
Given an \inftycategory C, there is an isomorphism h(C) \to \pi(C) of categories.
Daniel Davis 
11 November 2016
Given an \inftycategory C, more on the category \pi(C), and equivalences in C.
Daniel Davis
Topology Seminar Archive
 Spring 2016 archive
 Fall 2015 archive
 Spring 2015 archive
 Fall 2014 archive
 Spring 2014 archive
 Fall 2013 archive
 Spring 2013 archive
 Fall 2012 archive
 Spring 2012 archive
 Fall 2011 archive
 Spring 2011 archive
 Fall 2010 archive
 Spring 2010 archive
 Fall 2009 archive
 Spring 2009 archive
 Fall 2008 archive
 Spring 2008 archive