PhD position in Mathematics of Spatial Networks

Would you like to develop the mathematical theory of spatial networks and link their global behaviour to local constraints?

Use graphs, probability, and differential equations to develop the mathematical theory of spatial networks and link their global behaviour to local constraints. Join us as PhD candidate.

In recent years, there has been a significant surge of interest in networks, which now play a fundamental role in modern science and society. The network-like structures are widely discussed, from cosmology and communication to economics and ecology. Even at the nanoscale, in materials science, they may offer potential theoretical explanations for material properties. Despite their popularity, the mathematical foundations underlying networks remain incompletely understood. Spatial networks are especially challenging as they derive their graph-theoretical properties from local constraints imposed by the embedding metric space.

The aim of this fully funded PhD position is to develop the mathematical theory of spatial networks, and to explain why these networks exhibit specific emergent properties on a macro scale. Unlike conventional graphs, spatial networks exist within an embedding space, allowing us to consider well-defined scaling limits and to “zoom out,” viewing them as continua. Leveraging on the expertise of the network group in Utrecht, you will establish a framework for these limits and apply them to partial differential equations that arise. As such you will attempt to bridge the local topological constraints of networks with their global behaviour.

You will work as a member of the network group at Utrecht University, under the guidance of Dr Ivan Kryven. This position is part of the PRONTO consortium, which aims to advance models in materials science. Two related PhD positions are also being initiated at the University of Amsterdam concurrently, and regular exchange of expertise with your peers from the consortium will provide beneficial growth environment. We anticipate that project’s results will be relevant to other disciplines. Notably, this will give you an opportunity for discussing and communicating your own findings with collaborators, consortium partners and experts in industry.

In this PhD position you will:

• conduct research in spatial networks;
• publish research findings in scientific journals;
• get the opportunity to attend scientific conferences and workshops abroad;
• communicate the findings with our consortium partners and partners in industry;
• undertake a modest teaching load at the Mathematical Institute at Utrecht giving you the opportunity to gain teaching and student supervision experience.

You have a passion for mathematical research and are enthusiastic to make your contribution. With your collaborative attitude and good command of spoken and written English, you are able to contribute to effective cooperation with colleagues and collaboration partners in the research project. You hold a Master’s degree in mathematics or related discipline. If you are close to completing your degree, you are also welcome to apply. We see it is an advantage if you are familiar with graph theory, random graphs, stochastic processes, statistical mechanics or partial differential equations. Familiarity with one the programming languages, for example, Python or Matlab is also seen as an advantage. Willingness and ability to communicate one’s own findings to general audience is appreciated.

We offer:

• a position for four years; 
• a working week of 38 hours and a gross monthly salary between €2,770 and €3,539 in the case of full-time employment (salary scale P under the Collective Labour Agreement for Dutch Universities (CAO NU)); 
• 8% holiday pay and 8.3% year-end bonus; 
• a pension scheme, partially paid parental leave and flexible terms of employment based on the CAO NU. 

In addition to the terms of employment laid down in the CAO NU, Utrecht University has a number of schemes and facilities of its own for employees. This includes schemes facilitating professional development, leave schemes and schemes for sports and cultural activities, as well as discounts on software and other IT products. We also offer access to additional employee benefits through our Terms of Employment Options Model. In this way, we encourage our employees to continue to invest in their growth. For more information, please visit working at Utrecht University.

A better future for everyone. This ambition motivates our scientists in executing their leading research and inspiring teaching. At Utrecht University, the various disciplines collaborate intensively towards major strategic themes. Our focus is on Dynamics of Youth, Institutions for Open Societies, Life Sciences and Pathways to Sustainability. Sharing science, shaping tomorrow.

At the Faculty of Science there are 6 departments to make a fundamental connection with: Biology, Chemistry, Information and Computing Sciences, Mathematics, Pharmaceutical Sciences and Physics. Each of these is made up of distinct institutes that work together to focus on answering some of humanity’s most pressing challenges. More fundamental still are the individual research groups – the building blocks of our ambitious scientific projects.

The Mathematical Institute in the department of Mathematics is internationally recognised for its research in both pure and applied mathematics. It houses the Utrecht Centre for Mathematical Modelling and maintains a long-standing tradition of transdisciplinary collaboration with other scientific fields including, among others, atmosphere/ocean sciences, computational life sciences, mathematical biology, medical and seismic imaging, and theoretical physics.

The Mathematical Institute has close ties with the Departments of Biology, Physics, Information and Computing Sciences, the Faculty of Geosciences, UMCU (Utrecht University Medical Center), and institutes such as IMAU (Institute for Marine and Atmospheric research), RIVM (The Dutch National Institute for Public Health and the Environment) and CWI (the National Research Institute for Mathematics and Computer science). We participate in university focus areas in Complex Systems and Applied Data Science. The institute organises and teaches the Bachelor's curricula in Mathematics as well as the (English-taught) Master's programme. The institute currently comprises about 40 faculty members, 11 Postdocs, and 29 PhD candidates, and teaches 500 students.

If you are unsure whether you are eligible, please do not hesitate to get in touch with us directly through an informal inquiry to i.kryven@uu.nl.

Do you have a question about the application procedure? Please send an email to science.recruitment@uu.nl.

The interviews will take place during 15-19 July.

As Utrecht University, we want to be a home for everyone. We value staff with diverse backgrounds, perspectives and identities, including cultural, religious or ethnic background, gender, sexual orientation, disability or age. We strive to create a safe and inclusive environment in which everyone can flourish and contribute.

If you are enthusiastic about this position, just apply via the 'Apply now' button Please enclose:

• your letter of motivation;
• your curriculum vitae;
• academic transcripts;
• a sample of your research writing (for example, thesis, paper, report).

If this specific opportunity isn’t for you, but you know someone else who may be interested, please forward this vacancy to them.

Some connections are fundamental – Be one of them