It is a natural property of stochastic dynamical systems to exhibit several co-existing, metastable regimes in state space, alternating between order and chaos and, thereby, different time scales of predictability. Famous examples include various states in the transition to turbulent fluid flow or metastable chemical configurations. However, such transient stochastic phenomena cannot yet be rigorously described by classical random dynamical systems theory which focuses on an asymptotic description of order and chaos in globally simplified settings.

Advancing tools from dr. Engel’s previous research (see example references [1,2,3,4]), the team will introduce a new distinction into a localized and global analysis, enabling a rigorous approach to transient random dynamics. You will work on quantifying the typical times of observability for the different transient phenomena and elaborating criteria for a dynamically optimal decomposition of the state space into such local areas of interest. The key goal will be a completely new variational formula, balancing survival times and variability of the dynamical properties. As a postdoctoral researcher, you will be collaborating closely with the PhD student and Maximilian Engel, as well as developing your own research initiatives and (inter)national network.

Tasks and responsibilities: 

• Conduct research within the specified project, as described above.
• Interact with the PhD student
• Disseminate your research findings through publications in academic journals and through presentations at international conferences.
• Participate in relevant seminars and engage in research collaborations locally and/or internationally.
• Participate in the department’s educational programs, by teaching one single-semester course per year.

Example references:

For the application, you are not expected to study the following references in depth, but you may look into them for a high-level impression of the style of research:

• [1] Z. Adams, M. Engel and R. Gvalani. Separation of time scales in weakly interacting diffusions, arxiv, pp. 1-30, submitted preprint, 2025.
• [2] A. Blessing, A. Blumenthal, M. Breden and M. Engel. Detecting random bifurcations via rigorous enclosures of large deviations rate functions, Physica D: Nonlinear Phenomena, 476: 134617, 2025.
• [3] A. Blumenthal, M. Engel and A. Neamtu. On the pitchfork bifurcation for the Chafee-Infante equation with additive noise.  Probability Theory and Related Fields, 187: 603-627, 2023.
• [4] M.M. Castro, D. Chemnitz, H. Chu, M. Engel, J.S.W. Lamb and M. Rasmussen. The Lyapunov spectrum for conditioned random dynamical systems, to appear in Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2024+.

We are looking for an enthusiastic and driven candidate who meets the following requirements:

Your experience and profile:

• PhD in mathematics, with thesis submitted before the start of the Postdoctoral position.
• Publications in some subareas of analysis, probability theory and/or dynamical systems
• Interests: You should have a strong interest to develop new theory in random/stochastic dynamical systems and analysis
• Communication skills: You should have excellent written and verbal communication skills in English.
• Teamwork and independence: You should be highly motivated and committed to your research. While you should be able to work independently, you should also have a cooperative attitude and be willing to collaborate with the team members or other researchers, also from other (potentially more applied) fields.
• Teaching: You should be able to contribute to the department’s educational programs.

Good programming skills are a plus, as is prior knowledge of metastability and random dynamical systems.

A temporary contract for 38 hours per week for the duration of 24 months with a probationary period of two months. The preferred starting date is between September 1, 2025 and April 1, 2026. The gross monthly salary, based on 38 hours per week and dependent on relevant experience, ranges between €3,378 to €5,331 (scale 10). In addition you will receive an 8% holiday allowance and 8,3% year-end allowance. A favourable tax agreement, the ‘30% ruling’, may apply to non-Dutch applicants.  The Collective Labour Agreement of Universities of the Netherlands is applicable.