PhD Studentship: Universality in Random Growth Models

The University of Manchester - Department of Mathematics

Qualification Type:PhDLocation:ManchesterFunding for:UK StudentsFunding amount:£20,780 annual tax free stipend for 2025/26, plus full tuition fees.Hours:Full TimePlaced On:10th December 2025Closes:10th March 2026

UK students

This 3.5 year PhD project is fully funded and home students, and EU students with settled status, are eligible to apply. The successful candidate will receive an annual tax-free stipend set at the UKRI rate (£20,780 for 2025/26) and tuition fees will be paid. We expect the stipend to increase each year.

We recommend that you apply early as the advert may be removed before the deadline.

A modern area of research within probability theory is the study of a class of models named after Kardar, Parisi and Zhang and referred to as KPZ. This includes mathematical models for the random movement of interfaces that can be used as a model for the growth of a bacterial colony or the spread of a burning front. The KPZ class of models is deeply connected to other areas of mathematics including the length of the longest increasing subsequence in a randomly chosen permutation. This project will study universality within the KPZ class of models. The classical example of universality is the frequent appearance of the normal distribution in nature. This is justified mathematically by the central limit theorem. More generally, universality is the property that the large-scale behaviour of some system is independent of the microscopic details. The aim of the project will be to prove results extending our current understanding of universality in the context of the KPZ class of models.

A useful background for this project would be a good background in probability modules such as martingales, Markov chains, stochastic calculus or Brownian motion.

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline.

To apply, please contact the main supervisorDr William Fitzgerald - william.fitzgerald@manchester.ac.uk. Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project.