abstract: 1. Asymptotically symmetric Einstein manifolds. I shall give an introduction to the subject, focusing on the correspondence between Einstein metrics and their conformal boundaries.
2. A new eta invariant for CR 3-manifolds. I apply ideas from the correspondence conformal metricsEinstein metrics to define a new invariant for strictly pseudoconvex CR 3-manifolds (joint work with Marc Herzlich).
3. Selfduality. I shall explain results characterizing boundaries of selfdual Einstein metrics.