2016/2017

Several Complex Variables and Complex Dynamics

Mathematics

Principal investigators

Erlend Fornæss Wold

Professor
University of Oslo (UiO)
Year at CAS

Berit Stensønes

Professor
Norwegian University of Science and Technology (NTNU)
Year at CAS

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

Leandro Arosio

Post doc
University of Rome
Year at CAS

Filippo Bracci

Professor
University of Rome, Tor Vergata
Year at CAS

John Erik Fornæss

Professor
Norwegian University of Science and Technology (NTNU)
Year at CAS

Franc Forstneric

Professor
University of Ljubljana
Year at CAS

Josip Globevnik

Professor Em.
University of Ljubljana
Year at CAS

Frank Kutzschebauch

Professor
University of Bern
Year at CAS

Finnur Larusson

Professor
University of Adelaide
Year at CAS

Laszlo Lempert

Professor
Purdue University
Year at CAS

Erik Løw

Professor
University of Oslo (UiO)
Year at CAS

Han Peters

Associate Professor
University of Amsterdam
Year at CAS

Nikolay Shcherbina

Professor
University of Wuppertal
Year at CAS

Liz Vivas

Assistant Professor
Ohio State University
Year at CAS

News

Their mathematics is already used outside the mathematical sphere, from calculating an asteroid’s position to measuring the size of an iceberg, but Berit Stensønes believes it is only the beginning of the developments and applications of these powerful tools.

Every semester, CAS fellows are challenged to present their research to the other project groups at lunch-time seminars. For the pure mathematicians, having to explain their work to the uninitiated might be considered something of a challenge.