Symmetric spectra seminar

Sheffield-Warwick joint seimnar on modern foundations of stable homotopy theory

Description

In this seminar we want to understand some modern categories of spectra equipped with associative and commutative smash products which descend to the usual smash product in the stable homotopy category. We will concentrate on symmetric spectra, and follow the "Untitled book project about symmetric spectra" by Stefan Schwede [S] and any other relevant material subject to the participants' decisions. An advantage of symmetric spectra is that their construction does not require very advanced machinery. Then we will move on to the homotopy theory of symmetric spectra. We also talk about other things we like.

The seminar is aimed mainly at postgraduates and young researchers interested in algebraic topology, but of course everyone is welcome to attend.

In 2011/12 we meet every other week, on Wednesdays. There are three talks per meeting.

Participants

Magdalena Kedziorek (Sheffield)
Arjun Malhotra (Sheffield)
Michal Adamaszek (Warwick)
Rupert Swarbrick (Warwick)
Robert Goss (Warwick)

References

[S]: S. Schwede, An untitled book project about symmetric spectra, PDF
[HSS]: M. Hovey, B. Shipley, J. Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000), no. 1, 149-208, link
[G]: J. Greenlees, Spectra for commutative algebraists, Cont. Math. 436 (2007) 239-275, PDF
[K]: A.P.M. Kupers, Symmetric spectra, PDF
[H]: M. Hovey, Model categories
[EKMM]: Elmendorf, Kriz, Mandell, May, Cole Rings, Modules and Algebras in Stable Homotopy Theory

Schedule of talks:

Date	Speakers	Topic	References
22/11/2010 Sheffield	John Greenlees	History and overview
	Michal Adamaszek	Symmetric spectra: definitions, examples, basic properties	[S], I.1, I.2.1, [K]
	Michal Adamaszek	Symmetric spectra: definitions, examples, basic properties (cont.)
29/11/2010 Warwick	Magdalena Kedziorek	More examples and constructions	[S], I.2.1, I.2.2
	Magdalena Kedziorek	More examples and constructions (cont.)
	Rupert Swarbrick	Smash product	[S], I.3
06/12/2010 Sheffield	Rupert Swarbrick	Smash product (cont.)
	Michal Adamaszek	Semistability	[S], I.4
	Michal Adamaszek	Semistability (cont.)
17/01/2011 Warwick	Michal Adamaszek	Various conditions for semistability	[S], I.4
	Magdalena Kedziorek	Injective spectra and the stable homotopy category	[S], II.1, II.2
	Magdalena Kedziorek	Stable homotopy category (cont.)
24/01/2011 Sheffield	Magdalena Kedziorek	Additivity of the stable homotopy category
	Rupert Swarbrick	Triangulated categories and the st. hom. cat.
	Rupert Swarbrick	Triangulated categories and the st. hom. cat. (cont)
07/02/2011 Warwick	Rupert Swarbrick	Triangulated categories and the st. hom. cat. (cont)
07/02/2011 Warwick	Michal Adamaszek	Stable equivalences and s.h.c as localization	[S], II.4
28/02/2011 Sheffield	Michal Adamaszek	Derived smash product	[S], II.5
28/02/2011 Sheffield	Magdalena Kedziorek	Ho(M) is a HoSSet-module	[H], Ch. 4,5
25/03/2011 Sheffield	Rupert Swarbrick	Model categories of symmetric spectra	[S], III
25/03/2011 Sheffield	Michal Adamaszek	Hammock localization and function complexes	[DK]
11/04/2011 Warwick	Michal Adamaszek	Hammock localization cont.	[DK]
11/04/2011 Warwick	Magdalena Kędziorek	Spectra for commutative algebraists	[G]
09/05/2011 Sheffield	Rupert Swarbrick	Half-smash and orthogonal spectra	[EKMM]
23/05/2011 Sheffield	Rupert Swarbrick	Half-smash and orthogonal spectra	[EKMM]
23/05/2011 Sheffield	Magdalena Kędziorek	Algebraic Koszul duality
19/10/2011 Warwick	Magdalena Kędziorek	Koszul duality for operads
19/10/2011 Warwick	Michal Adamaszek	Ring spectra
02/11/2011 Sheffield	-
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Last modified 2011-10-26