Dirac Operator and Eigenvalues in Riemannian Geometry PROGRAM

Lecture 2. Index problem for manifolds with a boundary. Index of the Dirac operator and anomalies. Lecture 3. Spectral asymmetry and Riemannian geometry. Heat equation and asymptotic heat kernel. The η-and ζ-functions. Lecture 4. Two-component spinor calculus. Dirac and Weyl equations in two-component spinor form. Weyl equation with spectral or local boundary conditions. Potentials for massless spin-3 2 fields. (Refs. [4,5,6]) Lecture 5. Self-adjointness of the boundary-value problem for the Dirac operator in a particular class of Riemannian four-geometries with boundary. Asymptotic expansion of the corresponding heat kernel.