Stochastic analysis of many body systems

This project is one of a number that are in competition for funding from the University of Bath URSA competition for entry in September 2025.

Overview of the Research:

Systems involving large numbers of interacting bodies are commonplace in physics, chemistry, biology, social sciences and computer science. These systems often exhibit intrinsic chaotic behaviour as well as oftentimes being subject to external sources of noise. Common examples are systems taking place in a turbulent environment, measurement uncertainty when calibrating experiments and future uncertainty, particularly relevant in social science applications.

These features make the rigorous mathematical analysis of these systems highly challenging. Recent developments in pathwise stochastic analysis as well as new tools of ergodic theory have allowed for rapid progress towards a number of important mathematical results in the subject. This project will explore the possible regularising effect of both intrinsic and extrinsic noise on these systems to obtain new results on existence, uniqueness and stability of solutions to these systems. Further goals will be to study long time behaviour of particular systems and/or similar questions in the realm of stochastic partial differential equations (SPDE).

Project keywords: stochastic analysis, ordinary differential equations, stochastic differential equations, ergodic theory, functional analysis, nonlinear equations

Candidate Requirements:

Applicants should hold, or expect to receive, a First Class or high Upper Second Class UK Honours degree (or the equivalent) in a relevant subject. A master’s level qualification would also be advantageous.

Non-UK applicants must meet the programme’s English language requirement prior to a formal offer being made.

Enquiries and Applications:

Informal enquiries are encouraged and should be directed to Dr Avi Mayorcas

, am2735@bath.ac.uk. 

Formal applications should be submitted via the University of Bath’s online application form for a PhD in Mathematics prior to the closing date of this advert.

IMPORTANT:

When completing the application form:

1.      In the Funding your studies section, select ‘University of Bath URSA’ as the studentship for which you are applying.

2.      In the Your PhD project section, quote the project title of this project and the name of the lead supervisor in the appropriate boxes. 

Failure to complete these two steps will cause delays in processing your application and may cause you to miss the deadline.

More information about applying for a PhD at Bath may be found on our website.

Equality, Diversity and Inclusion:

We value a diverse research environment and aim to be an inclusive university, where difference is celebrated and respected. We welcome and encourage applications from under-represented groups.

If you have circumstances that you feel we should be aware of that have affected your educational attainment, then please feel free to tell us about it in your application form. The best way to do this is a short paragraph at the end of your personal statement.