Arjen Doelman – The Dynamics of Patterns

Arjen focuses his research on pattern formation, or in mathematical terms: the dynamics of solutions of nonlinear systems of evolutionary partial differential equations. The driving force behind his research is the rich cross-fertilization between mathematics and other research areas: his mathematical contributions are inspired by translating questions from, and observations in, other scientific fields into a mathematical framework, with his mathematical point of view he aims at providing fundamental novel insights in fields beyond mathematics. In that vein, he has contributed to neuroscience, bio-membranes, phytoplankton dynamics, the geophysics of sandbank generation and coastal evolution, and the hydrodynamics of tidal oscillations and internal (ocean) waves. His mathematical work especially concerns the existence, stability and dynamics of (interacting) localized structures in singularly perturbed systems. The present focus of his research is on ecosystem resilience, naturally in direct interaction with the mathematics of the dynamics of patterns.