PhD position in the topology of Hamiltonian systems (1.0 FTE)


Faculty of Arts


University of Groningen

Since its foundation in 1614, the University of Groningen has enjoyed an international reputation as a dynamic and innovative centre of higher education offering high-quality teaching and research. Balanced study and career paths in a wide variety of disciplines encourage currently more than 35,000 students and researchers to develop their own individual talents. Belonging to the best research universities in Europe and the top 100 universities in the world (see our ranking:, the University of Groningen is truly an international place of knowledge.

Within the Faculty of Science and Engineering (FSE), the Bernoulli Institute conducts research combining theoretical as well as practical aspects of three disciplines, namely Mathematics, Computer Science and Artificial Intelligence. The environment fosters truly interdisciplinary research with a great track record of national and international collaboration transferring knowledge across domains.

This PhD position is embedded within the research unit Dynamical systems, Geometry and Mathematical Physics (DSGMP) of the Mathematics department of the Institute. The research directions pursued at the DSGMP group cover a broad range of topics related to fundamental and applied aspects of Dynamical Systems and Geometry. This includes the study of Integrable and Chaotic Dynamical Systems, Quantum and Statistical Mechanics, Topology, Computational and Spectral Geometry; see for more information about our group.

Job description

Integral (or invariant) manifolds play an important role in the qualitative theory of Hamiltonian systems. After the works of Birkhoff and later Arnol’d and Smale, it has been realised that the topology and bifurcations of these manifolds have much to say about the geometry and dynamics of the underlying system, such as the presence of special types of singularities, the non-existence of cross-sections, etc.

This PhD project is focused on the study of integral manifolds in concrete examples of Hamiltonian systems, which arise in classical and celestial mechanics. A special emphasis will be placed on completely integrable systems and the Newtonian n-body problem. One central problem in this context is to understand the precise conditions that entail a non-trivial topology change of the integral manifolds in such systems and/or of certain singular fibrations made of such manifolds. For integrable systems, this may concern a change in the marked molecule invariants and various monodromy phenomena. For a general Hamiltonian system, such a change may arise as a result of the variation of the energy or an external control parameter.

We note that even though the main focus of the PhD project is on systems arising in mechanics, we expect the applicability of the results in a more general framework of dynamical systems, including for, example, port-Hamiltonian systems and dynamical systems on networks. Additionally, we expect this project to have implications for such fields as algebraic geometry, topology, and data science. Candidates with a background in (one of) these fields are therefore encouraged to apply.


The successful candidate should have:

· a Master’s degree in Mathematics or related area with excellent results
· an interest in Dynamical Systems and Topology
· demonstrable ability to learn a new subject
· experience in teaching and academic writing in English is a plus.

Conditions of employment

Contract length: 48 months.

The University of Groningen offers, in accordance with the Collective Labour Agreement for Dutch Universities:

· a salary of € 2,395 gross per month in the first year, up to a maximum of € 3,061 gross per month in the fourth and final year for a full-time working week
· a holiday allowance of 8% gross annual income and an 8.3% end-of-the-year bonus
· a full-time position (1.0 FTE) for the total period of four years. You will first be appointed for one year with the option of renewal for another three years. Prolongation of the contract is contingent on sufficient progress in the first year indicating a successful completion of the PhD thesis. A PhD training programme is part of the agreement.

The intended starting date is between 1 November 2021 and March 2022

Job Application

Application should include:

· a letter of motivation
· CV (including contact information for at least two academic references)
· transcripts from your Bachelor’s and Master’s degree.

The applicants are invited to submit their application until 2 August 23:59 pm / before 3 August 2021 Dutch local time by means of the application form (click on "Apply" below on the advertisement on the university website).

Applications received before the above date will receive full consideration; however, the position will remain open until filled.

We are an equal opportunity employer and value diversity at our University. We are committed to building a diverse faculty so you are encouraged to apply. Our selection procedure follows the guidelines of the Recruitment code (NVP), and European Commission's European Code of Conduct for recruitment of researchers,

Unsolicited marketing is not appreciated.

Additional information

For additional information, please contact:

Dr N. Martynchuk

In your application, please always include the job opening ID 221377

Digital application form