Large networks are one of the most popular but least understood objects studied in modern mathematics. They owe their popularity to numerous applications in physics, biology, computer and social sciences; however, the mathematical foundations of large networks are still being actively developed. One of the challenges mathematicians face when studying large evolving networks is that despite being discrete structures, they feature continuous-like properties that are reminiscent to differential equations: they converge to fixed points and experience bifurcation during continuous change of a parameter. A classic example is the ‘evolution’ of the Erdos Renyi graph if we interpret the connection probability as time. In this position, you as PhD candidate will seek explanation of this and more general phenomena by developing the theory of limiting differential equations in large evolving random graphs and studying properties of such equations. This position is a part of NWO VIDI funded project and expects close collaboration with a postdoc working on algorithmic aspects of network models as well as the rest of the Networks group at the Mathematical Institute at Utrecht.

As the PhD candidate, you will take part in:

• conducting research and publishing findings in the area of networks, graphs, differential equations and/or stochastic processes;
• providing modest teaching service in English.

We are looking for an inspiring and friendly PhD candidate to join the department of Mathematics. Preferably you find yourself in the following aspects: you are passionate about research in mathematics, you are excited to present your results to colleagues and at conferences, you are self-driven: willing to work independently and in collaboration with other group members.

You will bring the following in this position:

• You have an MSc degree in mathematics, applied mathematics, or a related discipline.
• Preferably your degree has emphasis on (partial) differential equations and probability, in particular analytical or numerical aspects of evolutionary problems, branching processes, or modelling with measures.
• Candidates in the final stage of obtaining this degree will also be considered.
• Having a good knowledge of Mathematica is considered an advantage.

• a position for four years;
• a full-time gross salary, ranging from €2,541 in the first year to €3,247 in the fourth year, in scale P (PhD-Promovendus);
• benefits including 8% holiday bonus and 8.3% end-of-year bonus;
• a pension scheme, partially paid parental leave, and flexible employment conditions based on the Collective Labour Agreement Dutch Universities (CAO).

In addition to the employment conditions laid down in the CAO for Dutch Universities, Utrecht University has a number of its own arrangements. For example, there are agreements on professional development, leave arrangements and sports. We also give you the opportunity to expand your terms of employment via the Employment Conditions Selection Model. This is how we like to encourage you to continue to grow.

More information about working at the Faculty of Science. 

Utrecht University is a friendly and ambitious university at the heart of an ancient city. We love to welcome new scientists to our city – a thriving cultural hub that is consistently rated as one of the world’s happiest cities. We are renowned for our innovative interdisciplinary research and our emphasis on inspirational research and excellent education. We are equally well-known for our informal atmosphere and the can-do attitude of our people. This fundamental connection attracts Researchers, Professors and PhD candidates from all over the globe, making both the university and the Faculty of Science a vibrant international and wonderfully diverse community.

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 problems. More fundamental still are the individual research groups – the building blocks of our ambitious scientific projects.

The Mathematical Institute in the department of Mathematics organises and teaches the Bachelor's curricula in Mathematics as well as the (English-taught) Master's programme in Mathematics and some service teaching in mathematics. The institute is internationally recognised for its research in both pure and applied mathematics. It houses the Utrecht Geometry Centre 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.