On the coefficients of a power series map between real-analytic hypersurfaces

A big part of research of A. Vitushkin in Several Complex Variables was dedicated to the study of $\mathrm{CR}$-maps. A number of interesting open questions are still remaining in the latter theory. In particular, properties of power series $\mathrm{CR}$-maps between real-analytic manifolds are still not understood completely. In this lecture, I will talk about recent developments in the theory of $\mathrm{CR}$-maps. In particular, properties of power series CR-maps have been understood completely in dimension 3 in the work of myself and my coauthors. We proved that power series under consideration always belong to so-called Gevrey classes, and moreover, they can be realized by asymptotic Gevrey series. Remarkably, these results can not be optimized further.

^* conference room 9th floor