# Juvitop Spring 2010

This is the Juvitop seminar webpage from Spring 2010, which was organized by Nick Rozenblyum and Anatoly Preygel about Twisted K-Theory and Loop Groups. This site was originally hosted here. This is part of a deep copy of all prior Juvitop websites that I could find in the fall of 2016.

Juvitop - Spring 2010

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".]

Schedule
DateSpeakerTitleNotes
02/17/2010Nick RozenblyumIntroduction
02/24/2010Rune HaugsengEquivariant K-Theory and Representation Theory
03/03/2010Dustin ClausenTwistings and Twisted K-Theory
03/10/2010Olga StroilovaLoop Groups
03/17/2010Anatoly PreygelThe Case of Tori(Soon.)
03/31/2010Rune HaugsengGroupoids
04/07/2010tbaConstructing the Map
04/14/2010tbaMore Representation Theory of Loop Groups

• 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)