Universality in random growth processes

About the Project

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.

Eligibility

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.

Funding

This 3.5 year project is open to home students. The successful candidate will receive an annual tax-free stipend set at the UKRI rate (£20,780 for 2025/26). Tuition fees will also be paid. We expect the stipend to increase each year.

We recommend that you apply early as the advert will be removed once the position has been filled.

Before you apply

We strongly recommend that you contact the supervisor(s) for this project before you apply. 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.

How to apply

Apply online through our website: https://uom.link/pgr-apply-2425

When applying, you’ll need to specify the full name of this project, the name of your supervisor, if you already having funding or if you wish to be considered for available funding through the university, details of your previous study, and names and contact details of two referees.

Your application will not be processed without all of the required documents submitted at the time of application, and we cannot accept responsibility for late or missed deadlines. Incomplete applications will not be considered.

After you have applied you will be asked to upload the following supporting documents:

• Final Transcript and certificates of all awarded university level qualifications
• Interim Transcript of any university level qualifications in progress
• CV
• Supporting statement: A one or two page statement outlining your motivation to pursue postgraduate research and why you want to undertake postgraduate research at Manchester, any relevant research or work experience, the key findings of your previous research experience, and techniques and skills you’ve developed. (This is mandatory for all applicants and the application will be put on hold without it).
• Contact details for two referees (please make sure that the contact email you provide is an official university/work email address as we may need to verify the reference)
• English Language certificate (if applicable)

If you have any questions about making an application, please contact our admissions team by emailing FSE.doctoralacademy.admissions@manchester.ac.uk.