K-theory Loop Groups and moduli of principal bundles on Riemann surfaces

- Plan of the course. Topological K-theory. The Index theorem. Older notes: Moduli of bundles, Verlinde TQFT
- Twisted K-theory using Fredholm operators
- Gerbes. Mayer-Vietoris calculations.
- Chern character and its twisted versions
- K_G(G). Weyl character formula. Graded twistings
- Moduli of G-bundles
on a Riemann surface and the universal index formula (KITP, 2003)

The full and chiral WZW models (MSRI, 2014) - Group laws and cohomology theories (Mistakes fixed, almost ready)
- Twisted
*K*-theory and equivariant elliptic cohomology

- Hatcher: Vector bundles and
*K*-theory. - Atiyah:
*K*-theory - Segal: Equivariant K-theory (IHES Publications
**34**, 1968) - Atiyah, Segal: Equivariant K-theory and Completion, J. Diff Geometry
- Freed, Hopkins: Teleman, Loop Groups and K-theory I, J. Topology
**4**(2011) - Donovan, Karoubi: IHES Publications
**38**, 1970 (torsion twistings) - Bouwknegt, Carey et al: Twisted
*K*-theory and K-theory of bundle gerbes, CMP**228**(2002) - Atiyah, Segal: Twisted
*K*-theory 1, 2; Ukr. Math. Bull 1, 2004 - Freed, Hopkins, Teleman: Twisted equivariant K-theory with complex coefficients, J. Topology
**1**, 2008 - Freed's ICM lecture
- Lurie, A survey of elliptic cohomology