Network archaeology in random trees

Supervised by Dr Bas Lodewijks and Dr Jonathan Jordan.

The University of Sheffield is one of the leading Russell Group universities in the UK. We carry out cutting-edge research with strong links to industry. When you enrol to do a PhD with us, you will be working with world-leading academics and have access to top of the range facilities. As a PhD student you will have the opportunity to gain skills not only to conduct research, but also to take your career to the next level, whether you want to stay in academia, go into industry or the public sector, or set up your own company. You will have access to a range of training and support services to help you excel in your studies and beyond.

Project Description

This 3.5-year studentship is part of the School of Mathematical and Physical Sciences at the University of Sheffield, within the Probability Theory research group. The project focusses on network archaeology in random trees, particularly preferential attachment trees with vertex removal. Network archaeology studies the problem of reconstructing the temporal history of a network when only its final state is observed. Understanding network evolution provides insight into its present structure and has applications in network science, biology (e.g. protein–protein interaction networks), and computer science. From a mathematical perspective, network archaeology presents interesting combinatorial, graph theoretical, and probabilistic problems, and hence has recently seen a wealth of activity in the (combinatorial) probability community, mostly in the setting where the underlying network dynamics generate trees.

Most mathematical work on network archaeology for random trees focuses on root finding, using only the observed tree structure. Here, given a tree T and accuracy \epsilon, the goal is to output a (minimal) subset S of vertices in T such that the probability that the root is within the set S is at least 1-\epsilon. The size K=K(\epsilon) of the set S is known as the budget. Optimality of the order of the budget K in terms of \epsilon is a further goal. Interestingly, for many different tree models there exist algorithms that require a finite budget K, irrespective of the size of the tree.

The studentship will generate impact by extending current state-of-the-art research regarding root finding to the more general setting of preferential attachment trees with vertex removal, as well as by tackling new problems within network archaeology on random trees. Students are valued and active members of the School and will be part of a wider network of PhD students. You will have the chance to influence and lead school activity, seminars and events, and meeting leaders in the field. The university offers, in addition to supervision, rigorous research and scholarly training throughout your PhD, as well as funding to travel to and attend summer schools, workshops, and conferences. The probability group at the university of Sheffield has close contacts with other research groups within the UK, for example via the `Probability in the NorthEast’ consortium. The university also hosts the Applied Probability Trust, thus leading to an increased activity in terms of event organisation.

Beyond academia, Sheffield is a medium-sized city, notably the greenest city in the UK, offering reasonably affordable housing, a vibrant city centre with a large independent scene, and easy access to nature in the Peak District.

How to apply

Interested candidates are strongly encouraged to contact the project supervisors to discuss your interest in and suitability for the project prior to submitting your application.

Please refer to the EPSRC DLA webpage for detailed information about the EPSRC DLA and how to apply.

Applicants must ensure that they use the correct application form linked to the EPSRC DLA webpage and must submit an application for October 2027 entry. The form is unique to the EPSRC DLA. It contains the list of advertised projects from which to select, and three questions specific to the DLA.

The application deadline is 17:00 GMT 13 January 2027.

The majority of our DLA studentships will be allocated to candidates who qualify for Home fee status, in accordance with EPSRC funding regulations which place strict limits on international recruitment.

Funding Notes

The award will fund the full tuition fee and a maintenance stipend at the UKRI rate (currently £21,805 per annum) for 3.5 years, as well as a research grant to support costs associated with the project.