Several Complex Variables and Complex Dynamics
Several Complex Variables and Complex Dynamics
Principal investigators
Abstract
This project explored the interplay between Several Complex Variables, Complex Dynamics, and modern Oka theory—three areas of complex analysis with deep geometric and topological implications. Central to the work was the study of the Cauchy-Riemann equations and the role of positivity in finding flexible solutions in complex geometric settings. The team investigated the Oka principle, where certain analytic problems have only topological obstructions, and applied this to the classification of holomorphic mappings between complex manifolds. Connections were also drawn to Andersén-Lempert theory and the structure of automorphism groups of complex spaces. In Complex Dynamics, the project examined the long-term behavior of holomorphic systems and the surprising role of flexibility in understanding dynamical stability. The collaboration led to several significant results and initiated new directions for future research, including a joint application for a European ERC synergy grant.
Fellows
John Erik Fornæss