Lecture 1: A review of ``Attractors and Arithmetic.''
Describe the attractor mechanism. Explain how it
selects calabi-yau compactifications associated with
complex multiplication, in the known exact solutions.
Say something about how RCFT's correspond to K3
surfaces with complex multiplication in F-theory.
Lecture 2: A review of ``Black Hole Farey Tail.''
Very brief review of AdS/CFT. Explain
in the case of AdS3 x S3 x K3 how the
dual CFT is a sigma model with target space
HilbN(K3). Compute elliptic genus of this.
Explain that the Rademacher-Petersson
expansion of Fourier coefficients of modular
forms (and Jacobi forms)
can be interpreted as a formula for the
elliptic genus in terms of a sum over BTZ
black holes, giving an explicit example of
an exact AdS/CFT relation.
Lecture 3: E8 gauge theory and the M-theory C-field.
Brief review of 11d sugra. Explain that the gauge
equivalence class of the 3-form field (C) is given
by Cheeger-Simons cohomology (a.k.a. Deligne
cohomology). Give the E8 model for the C-field
and formulate the 11d sugra action in topologically
nontrivial G-flux, and on a boundary in terms of
E8 gauge theory. Derive the
Gauss law for the path integral on a manifold with
boundary. Explain some applications.
