Talbot 2010

Mentored by Constantin Teleman of UC Berkeley

The workshop will constitute a weeklong retreat with talks and organized discussions during the mornings and evenings; the afternoon schedule will be kept clear for informal discussions and collaborations. The workshop will generally focus on understanding the relationship between the representation theory of a loop group LG and the equivariant twisted K-theory of G. Specifically, talks will develop the geometric approach to the representation theory of loop groups, K-theory and its twisted variant, basic computations of K-theory, Dirac operators and the families index theorem, extended topological field theories and Chern-Simons theory, conformal field theory and the WZW model, and recent work on extending Chern-Simons and gauged Gromov-Witten theory.

Below are some very preliminary references for the 2010 Talbot workshop.

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)

  • Bartels-Douglas-Henriques conformal nets (arxiv)

What is the Talbot Workshop? The Talbot Workshop is a weeklong workshop for young researchers. The week will be comprised of talks by participants and organized discussions during the mornings and evenings. The afternoon schedule will be kept clear for informal discussions and collaborations. The workshop discussions will have an expository character and will be aimed at graduate students and junior faculty interested in this year's workshop topic. At the same time, the workshop will host a diverse array of participants with varying backgrounds.

Who should apply? The Talbot Workshop seeks to gather a diverse array of young researchers--as such, there is no strict prerequisite on an applicant's mathematical background. Those working outside the field of topology, young graduate students, and other non-experts are encouraged to apply. In the end, we will seek a good mixture of experts and non-experts.

Do I have to give a talk at the workshop? A little more than half the participants of the Talbot Workshop will be giving a talk. These talks are not meant to be talks on original research, and will be assigned based on the background of the participants.

How much funding can I receive from the workshop? This year's Talbot Workshop is generously supported by the NSF, but we will have limited funding and space at the workshop site. Our goal is to fund participants who require financial assistance, but we cannot guarantee funding for all.

When is the application deadline? Applications must be submitted by midnight on the night of January 31st, EST.

When will I know if I can be supported? We will inform participants of their acceptance, along with information regarding funding, by mid-February.

What if I have other questions? Please contact talbotworkshop(at)gmail.com with any questions. We will reply as soon as we can to any questions or requests, but please allow for up to a week for a response.