Juvitop - Spring 2010

About

Juvitop is the MIT graduate student topics seminar in algebraic topology. The topic for this semeser is "Twisted K-Theory and Loop Groups", in preparation for this year's Talbot workshop on the same.

*Announcement*: There will be no meeting on March 24th, due to MIT spring break.

At least for the time being the seminar will meet at an unusual time-and-place:

When: Wednesdays at 7 pm
Where: Near Central Square:
107 Columbia Street (Map),
Apt. 2

You might also want to check out last semester's juvitop, babytop, or the topology seminar.

Questions/Comments? Email one of the organizers: Anatoly Preygel (preygel at m@h.mit.edu) or Nick Rozenblyum (nrozen at m@h.mit.edu). [Replace "@" with "at".]

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Schedule

Date	Speaker	Title	Notes
02/17/2010	Nick Rozenblyum	Introduction
02/24/2010	Rune Haugseng	Equivariant K-Theory and Representation Theory
03/03/2010	Dustin Clausen	Twistings and Twisted K-Theory
03/10/2010	Olga Stroilova	Loop Groups
03/17/2010	Anatoly Preygel	The Case of Tori	(Soon.)
03/31/2010	Rune Haugseng	Groupoids
04/07/2010	tba	Constructing the Map
04/14/2010	tba	More Representation Theory of Loop Groups

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References and Related Reading

K-Theory: Atiyah's "K-Theory" (and the appendix on the Fredholm operators picture). Lots of others...
Representation theory of compact Lie groups: Lots of places. Including Ch. 2 of Pressley-Segal (see below).
Equivariant K-Theory: To be added. Equivariant K-theory and completion by Atiyah, Segal.
Stacks/Gerbes: To be added. (Do we need this?)
Twisted K-theory: Twisted K-theory, Twisted K-theory and cohomology by Atiyah, Segal.
"Loop Groups" by Pressley, Segal.
Freed, Hopkins, Teleman on Twisted equivariant K-theory with complex coefficients.
The Freed, Hopkins, Teleman three-parter on the relation to the Verlinde ring: Loop groups and twisted K-theory I, Loop groups and twisted K-theory II, Twisted K-theory and loop group representations (aka "... III").
Freed, Hopkins, Lurie, Teleman on extending 3-dimensional Chern-Simons (for finite groups/torii): Topological Quantum Field Theories from Compact Lie Groups.

This will eventually be link-ified and merged with the above, but for now here's the preliminary reference list provided by Teleman:

			References for Talbot (very preliminary)

			Basic:
			Hatcher, Vector bundles and K-theory. On his webpage.
			Atiyah, K-theory.
			Segal, Equivariant K-theory (IHES 69?)
			Atiyah-Segal, Completion theorem (J Diff Geom 84?)
			FHT (=Freed-Hopkins-Teleman) 1, Appendix for K-theory of stacks (arxiv)

			Twistings and twisted K-theory:
			Donovan-Karoubi IHES (torsion twistings)
			Carey et al, CMP early 2000's
			Atiyah-Segal 1,2
			FHT -- Complex equivariant K-theory, J Topology
			FHT 1,2,3
			Freed's ICM lecture
			Ando, Blumberg, Hopkins et al: units in ring spectra

			Loop groups, representations, CFT:
			Pressley-Segal;
			Kac, for lie algebras esp. twisted affine algebras if covered
			Segal's notes on CFT (Proceedings of 2002 conference)
			Segal's paper for loops in torus (?? refs)
			I. Frenkel: Orbital theory for affine Lie algebras. Invent. Math. 77 (1984)

			Additional Topics:
			Grojnowski-Rosu-Ando et al for equivariant elliptic cohomology over C?
			Jacob if anything available? (But Jacob would cover that anyway)

			Open-closed theory, Landau-Ginzburg potentials
			To be added depending on how much we cover
			Gauged string topology
			If a paper available, perhaps me or one of my students

			Relation to Chern-Simons:
			Freed-Hopkins-Lurie-Teleman for the torus (arxiv)
			Douglas-Henriques conformal nets (arxiv)