Szego projections and new invariants for CR and contact manifolds
  In this paper we give a survey of the constructions in math.DG/0510061 of several new invariants for CR and contact manifolds. The latter extend previous constructions of Hirachi and Boutet de Monvel. In addition, we give simple algebro-geometric arguments proving that Hirachi's invariant vanishes on strictly pseudoconvex CR manifolds of dimension 4m+1. 
Raphael Ponge