Chiral conformal field theory

Course notes

  video1 [15min] (different notions of CFT)
Riemann surfaces with boundary
  video2 [18min] (complex cobordisms)
  video3 [37min] (conformal welding)
  video4 [29min] (cobordisms with thin parts)
  video5 [35min] (moduli of cobordisms)
Definition of chiral CFT
  video6 [30min] (full vs chiral CFT)
  video7 [13min] (algebras of observables)
  video8 [34min] (disjoint union and tensor product)
  video9 [18min] (the vacuum sector)
  video10 [29min] (the fusion product)
Central extensions
  video11 [21min] (central extensions of the semigroup of annuli)
  video12 [37min] (the Virasoro algebra)
  video13 [49min] (the cohomology of the Witt algebra)
  video14 [39min] (the holomorphicity condition)
  video15 [51min] (Ann(S¹) as complexification of Diff(S¹))
  video16 [37min] (integrating the Virasoro cocycle)
Examples of chiral CFTs
  video17 [32min] (loop groups)
  video18 [25min] (minimal & WZW models)
  video19 [36min] (spin CFTs)
  video20 [36min] (the chiral free fermion CFT)
  video21 [21min] (functors associated to cobordisms)
The positive energy condition
  video22 [40min] (trace class maps and the positive energy condition)
  video23 [16min] (thick cobordisms and trace class maps)
  video24 [44min] (trivializing the annulus functors)
Representation theory
  video25 [37min] (representations of Virasoro)
  video26 [23min] (structure of finite dimensional simple Lie algebras)
  video27 [30min] (representations of finite dimensional simple Lie algebras)
  video28 [51min] (affine Lie algebras)
  video29 [68min] (the Sugawara construction)
  video30 [61min] (the Sugawara construction - proofs)