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.
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.
15 September 2017
More about the Goerss-Hopkins Linearization Hypothesis and a connection to continuous G-spectra.
22 September 2017
The Goerss-Hopkins Linearization Hypothesis and continuous G-spectra, part 3.
For the Spring 2017 semester we will meet at 1:00 on Fridays in 208 Maxim Doucet Hall.
27 January 2017
Genuine equivariant operads
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
10 February 2017
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.
23 September 2016
Infinity-categories: more on the example of small categories and infinity-categorical versions of basic category-theoretic notions.
30 September 2016
Some examples of infinity-categorical concepts that build on category-theoretic notions.
14 October 2016
The notions of join and overcategory in the setting of infinity-categories.
21 October 2016
Simplicial nerves and the homotopy category of an infinity-category.
28 October 2016
The homotopy category of an infinity-category and a nicer formulation of it.
4 November 2016
Given an \infty-category C, there is an isomorphism h(C) \to \pi(C) of categories.
11 November 2016
Given an \infty-category C, more on the category \pi(C), and equivalences in C.
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