Holomorphic rigidity of totally nondegenerate CR manifolds

After presenting some required preliminaries concerning the two theories of Cauchy-Riemann (CR) manifolds and (Levi)-Tanaka transitive prolongations, I explain the application of the latter theory in proving Beloshapka’s maximum conjecture on the holomorphic rigidity of his totally nondegenerate CR models. As a consequence of the results, we observe in particular that all origin-preserving CR automprphisms of these models are linear. This talk is based on a joint work with Andrea Spiro.