Valid Until: 2026-12-31 23:59
Abstract: In the framework of analysis of several complex variables it is natural to identify biholomorphically equivalent geometrical objects. This is appropriate for everything: domains, its boundaries, singular subsets of boundaries (Shilov boundaries), orbits of holomorphic Lie group action, etc.
A germ of a real submanifold in complex space is a highly interesting object. There are three interrelated aspects of this interest: holomorphic automorphisms of the germ, its invariants and classification. These issues belong to CR geometry, which is a domain of interplay between different directions: complex analysis, differential geometry, Lie groups and algebras, theory of differential equations, algebraic geometry, invariant theory, and so on. CR geometry takes its origin in the seminal papers of H. Poincare and E. Cartan. Since then the two approaches in it have been crystallized: analytical, which develops the ideas of Poincare, and geometrical, developing that of Cartan. The author, working in the Poincare paradigm, is going to give a survey of the modern state of the analytical branch of CR geometry.
Bio: Professor Valerii K. Beloshapka graduated from the Department of Function Theory and Functional Analysis of the Faculty of Mechanics and Mathematics of Moscow State University in 1975. He defended PhD thesis in 1979 and his doctoral dissertation "Description of holomorphic automorphisms of real surfaces of high codimension" in 1991. He works at the Faculty of Mechanics and Mathematics since 1992 and became a Professor at the Department of Function Theory and Functional Analysis in 1996.
The main research area of Valerii Beloshapka is real submanifolds of complex spaces, their holomorphic automorphisms, classification and invariants. This problem organically combines the methods and approaches of multidimensional complex analysis, differential geometry and algebra.
Valerii Beloshapka was an invited speaker at many international conferences. Laureate of the Prize of Mathematics Department of USSR Academy of Sciences (1989). He is a fellow of the International Science Foundation (1993). In 1998 he got State Scientific Scholarship for Outstanding Scientists.