11.24.09:
Charles Rezk (
UIUC).
Koszul resolutions for algebras of power operations.
A Tuesday session of the main Topology seminar.
11.03.09:
Ricardo Andrade (
MIT).
a Tale of Hochschild Homology.
A simple narrative of $THH$ and $S^1$. A retelling of the old story
that brings forth a more meaningful relation.
10.27.09:
[Mark Behrens] (
MIT).
[Juvitop lecture - Babytop swapped with Wednesday]
10.13.09: - (Columbus Day). .
09.29.09:
Søren Galatius (
Stanford).
Monoids of moduli spaces of manifolds.
A Tuesday session of the main Topology seminar.
09.22.09:
Martin Frankland (
MIT).
Composite spectral sequence in the non-abelian context.
Last semester, I explained how resolution model categories allow us to use some machinery of homological algebra, such as derived functors, in the non-abelian context of homotopical algebra. Basically, cofibrant replacements play the role of projective resolutions.
One useful tool in homological algebra is the Grothendieck spectral sequence, which relates the derived functors of a composite to the derived functors of each individual functor. Does it have an analogue in homotopical algebra? Yes it does, as we will see in this talk.
No prerequisites from previous talks will be assumed.
09.15.09:
Matthew Gelvin (
MIT).
Fixed points and homotopy fixed points.
This will be a gentle introduction to the role of group-action fixed points in algebraic topology. After a brief discussion of $G$-sets, we will move on to talking about $G$-spaces, which will lead to the introduction of a homotopy-appropriate notion of the fixed point space. We will conclude with a discussion of the relationship between ordinary and homotopy fixed points.
This talk will be very not-rigorous, and I will try to avoid the temptation to prove much of anything.
Name dropping: Expect to hear mention of at least one Sullivan, one Segal, and maybe a Frattini.
