He worked as a postdoc at the Center for Applied Mathematics of Cornell University with Philip Holmes and had a position as assistant professor (`UD') in the `Applied Analysis' group of the Department of Mathematics of Utrecht University. He became professor of `Applied Analysis and Dynamical Systems' at the Korteweg-de Vries Institute for Mathematics of the University of Amsterdam in August 1998. This position was reduced to a one day a week position in the period September 2004 - January 2009. In September 2004, Arjen Doelman (partly) moved to a position at the Center for Mathematics and Computer Science (CWI), where he was head of the (CWI-)cluster Modelling, Analysis and Simulation (MAS) in the period January 2007 - December 2009. In February 2009, he became professor of Applied Analysis at the Mathematical Institute of Leiden University, in November 2009 he became director of the Lorentz Center. After almost 14 years, Arjen Doelman stepped down as director of the Lorentz Center in September 2023. Since then, he has a full-time position at the Mathematical Institute of Leiden University.
His main research interests are in the fields of nonlinear dynamical systems, pattern formation, singular perturbation theory and their applications (in oceanography, geophysics, chemistry, hydrodynamics, ecology, biology, etc.). In 2023, his research on pattern formation in ecology -- and especially on (the evasion of) tipping points in ecosystems -- culminated in the (joint) ERC Synergy project RESILIENCE
.