Randomness and random shapes can be found everywhere around us, for example the shape of a tree is influenced by random interactions both between and within its cells, and random external influences. This random growth causes trees in nature to have self-similar, fractal-like properties. Underlying random growth also makes our backyard oak look remarkably similar to other structures in nature and systems of human design, such as the shape of river systems; the circulatory system in animals; and the connectivity structure of the internet and digital social networks. Broccolis looking like trees is a consequence of a universality principle in random structures: the precise random dynamics of cell growth in the two organisms is different, but those differences have a negligible effect on the overall structure.

The goal of this PhD project is to examine universality in random trees and graphs. (Morally, you will rigorously prove what it takes to look like a broccoli.) The focus will lie on directed graphs (in which edges have directions) and dynamical trees and graphs (in which the connectivity structure evolves over time). This research requires the PhD candidate to develop new combinatorial sampling methods, and to use techniques from (stochastic) analysis to study limiting properties. The PhD candidate will acquire skills that are broadly applicable in combinatorics and analysis, and in discrete and continuous probability theory.

The objective of the temporary position is the production of a number of research articles in peer-reviewed scientific journals and conference proceedings, which together will form the basis of a thesis leading to a PhD degree (Dr) at the University of Groningen. The position comes with a light teaching duty. The candidate will become a member of the Probability and Statistics Group of the Mathematics Department and will work under the supervision of Serte Donderwinkel.

Organisation
Founded in 1614, the University of Groningen enjoys an international reputation as a dynamic and innovative institution of higher education offering high-quality teaching and research. Flexible study programmes and academic career opportunities in a wide variety of disciplines encourage the 34,000 students and researchers alike to develop their own individual talents. As one of the best research universities in Europe, the University of Groningen has joined forces with other top universities and networks worldwide to become a truly global center of knowledge.

The successful candidate should

- have a Master’s degree or equivalent in mathematics or another relevant field with sufficient mathematical content; preferably with a focus on combinatorics or probability theory
- have good English language and communication skills.

Fixed-term contract: 48 months.

We offer you, following the Collective Labour Agreement for Dutch Universities

- a salary of € 2,770 gross per month in the first year, up to a maximum of € 3,539 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% year-end bonus
- a full-time position (1.0 FTE).

The successful candidate will first be offered a temporary position of one year with the option of renewal for another three years. Prolongation of the contract is contingent on sufficient progress in the first year to indicate that a successful completion of the PhD thesis within the next three years is to be expected. A PhD training programme is part of the agreement and the successful candidate will be enrolled in the Graduate School of Science and Engineering.

Preferred starting date: September 1 (or in consultation with the candidate)