K-theory Loop Groups and moduli of principal bundles on Riemann surfaces
The lecture notes are preliminary and may contain mistakes. If you find any, feel welcome to email me.
  1. Plan of the course. Topological K-theory. The Index theorem.
  2. Older notes: Moduli of bundles, Verlinde TQFT
  3. Twisted K-theory using Fredholm operators
  4. Gerbes. Mayer-Vietoris calculations.
  5. Chern character and its twisted versions
  6. K_G(G). Weyl character formula. Graded twistings
  7. Moduli of G-bundles on a Riemann surface and the universal index formula (KITP, 2003)
    The full and chiral WZW models (MSRI, 2014)
  8. Group laws and cohomology theories (Mistakes fixed, almost ready)
  9. Twisted K-theory and equivariant elliptic cohomology
Some references: