Ilya Kossovskiy, Segre family approach to the classification of real-analytic hypersurfaces and applications

Ilya Kossovskiy (Masaryk University, Brno)

Title: Segre family approach to the classification of real-analytic
hypersurfaces and applications

Abstract: We demonstrate a new approach to constructing a normal form
for a real-analytic hypersurface in C^N, which via the Segre family of a
hypersurface. As an outcome, we are able: (i) to provide a new proof of
convergence of the Chern-Moser normal form; (ii) give a new point of
view on describing the well known Chern-Moser's chains; (iii) provide a
solution for an old problem of Poincare ("Probleme local").
This work is joint with P.Ebenfelt and B.Lamel.