Autumn 2019 schedule
| Date | Speaker | Topic |
|
8/20 |
Organization | |
|
8/27 |
Duncan Clark | A model for the Goodwillie derivatives of the identity functor |
|
9/3 |
Niko Schonsheck | Localization and completion with respect to topological Quillen homology |
|
9/10 |
Yu Zhang | What can be seen by topological Quillen homology? (notes) |
|
9/17 |
Michael Horst | Bicategorical limits (slides) |
|
9/24 |
Scott Newton | Id Types, Hom Types, and Higher Category Theory |
|
10/1 |
Ernie Fontes | Group completion, the plus construction, and S-inverse-S
Abstract: For a ring R, the algebraic K-theory groups K_n(R) admit many equivalent definitions. The higher groups (n bigger than 2) require constructing a space K(R) whose homotopy groups are K_n(R). We compare two definitions due to Quillen: On one hand, K(R) is the space K_0(R) x BGL(R)^+, where (-)^+ denotes a certain group completion. On the other, K(R) is the nerve of a certain construction, S-inverse-S, on the exact category of finitely-generated projective R-modules. We will discuss the correspondence between these two constructions and finish with a classical description of K_2(R) in terms of elementary matrices and commutators. (This will serve as a pre-talk for Thursday's Homotopy Seminar.) |
|
10/8 |
Duncan Clark | Colored operads and their algebras |
|
10/15 |
Scott Newton | Motivating Directed Type Theory From Directed Homotopy Theory |
|
10/22 |
Matt Carr | Dold-Kan Correspondence |
|
10/31* |
Matt Carr | lim^1 and Milnor exact sequences |
|
11/5 |
No Talk | |
|
11/12 |
Gabe Bainbridge | Algebraic Model Categories
Abstract: The examples of weak factorization systems (WFS) that homotopy theorists are most familiar with come from model categories. In fact a model category can be defined as two weak factorization systems (W \cap C, F) and (C, F \cap W) on a bicomplete category. One draw back of WFS's is that a functorial WFS on a category M does not induce a WFS on the functor category M^A objectwise. We will discuss functorial weak factorization systems where the left side is given by retracts of coalgebras for a comonad and the right side is given by retracts of algebras for a monad. These are called algebraic weak factorization systems (AWFS). The extra structure of an AWFS (L, R) allows the maps in R to encode lifting with respect to a category of maps in L, rather than just a set. Having this property allows us to put an objectwise AWFS on M^A. We will see how Garner's algebraic small object argument can be used to generate AWFS's, discuss algebraic model structures, and then look at the objectwise and projective model structures on the functor category M^A induced by an algebraic model structure on M. If time permits, I will briefly discuss some of my work towards a version of Bousfield localization for algebraic model categories. |
|
11/19 |
-- | -- |
|
11/26 |
Thanksgiving - No Talk | |
|
12/3 |
Niko Schonsheck | Long homology localization towers |
|
12/10 |
Final exam week - No Talk |
* denotes an unusual time or date