Model reduction via symmetries and conservation laws for systems on multiple time scales

The RTG Multiscale Clocks aims at investigating the principles of timekeeping in living organisms, enabling to orchestrate periodic processes with very different frequencies ranging from infradian over circadian to ultradian rhythms. The unique approach is to combine the expertise of biologists, physicists, chemists, mathematicians, and engineers to advance the understanding of biological clocks.

In this project (N°. 11), the PhD candidate will deal with different methods from applied mathematics and machine learning to analyse parametric differential equations modelling biological oscillators. Key goal is to combine symmetry theory and singular perturbation theory for the treatment of systems on multiple time scales. We aim at complementing traditional analytical approaches with novel data-driven methods from machine learning exploiting both numerical generated data and data obtained in experiments in other projects of the RTG. An important aspect of the project is to make all developed methods completely algorithmic and to implement them in software packages, which biologists can apply even if they do not have a deeper understanding of the underlying mathematics.

Tasks:

 - Scientific work on the research project.

 - Active participation in the workshops and events of the RTG and collaboration with the PIs and other PhD candidates.

 - Completion of a study program according to the curriculum of the graduate school.

Required Profile:

 - Excellent Master degree or other respectively related academic degrees (such as Diploma or Magister) in mathematics or a closely related field.

- Commitment to interdisciplinary research and education.

- Strong skills in English.

- Advantageous are experiences in one or more of the following topics: Dynamical systems, Lie symmetry theory, singular perturbation theory, model reduction, machine learning, computer algebra, numerical simulation.

The University of Kassel is a midsize university with about 25.000 students, located in the city of Kassel, known for the DOCUMENTA, the most important international exhibition of contemporary art. The university is dedicated to interdisciplinary research, and it offers educational programs in the life sciences, humanities, fine arts, social sciences, education, and engineering. The university also offers different employment benefits, such as free public transport and no tuition. Furthermore, housing in Kassel is affordable.

Please send your application with the usual informative documents, stating the reference number in the subject line, via the online form.

Include the Extra Application Form.