CR structures and general relativity

Prof. Denson C. Hill

1. Brief introduction to several complex variables.
2. Brief introduction to CR stuctures on manifolds.
3. Brief introduction to Einstein's equations in general relativity. Shear free congruences of null geodesics in 4-dim Lorentzian spacetimes.
4. Connection with the local embedding problem for 3-dim CR structures.
5. The intrinsic geometry of 3-dim congruences.
6. The Goldberg-Sachs theorem in a 4-dim spacetime, it's analogues in other signatures, and it's generalizations.