Royal Society PhD studentship: Eigenvalues of large random matrices and statistics of characteristic polynomials

A 4 year PhD studentship in mathematics, funded by the Royal Society.

Type of award: Postgraduate Research

PhD project: Eigenvalues of large random matrices and statistics of characteristic polynomials

Supervisor: Dr Nick Simm

The basic question of random matrix theory is the following. Given a large N x N matrix whose entries are random variables from a given probability distribution, what can be said about statistics of the eigenvalues / eigenvectors? This subject has seen spectacular developments over the last few decades, including the universality of spectral statistics, the relation to zeros of the Riemann zeta function and connections to statistical mechanics.

A central theme of this PhD project involves characteristic polynomials of random matrices. That said, the project is flexible and the precise research direction can be discussed, depending on the interests of the candidate.

The characteristic polynomial is believed to be connected to behaviour of the Riemann zeta function on its critical line. While this relation attracted a lot of interest, several aspects remain conjectural or mathematically unsolved. From a probabilistic point of view, typical fluctuations akin to a central limit theorem have been studied to some extent, but part of the project will be to understand different aspects of the fluctuations. It is also of interest to understand the large deviations and extreme value statistics.

The techniques involved to study these questions are a blend of analytical methods and probability theory. It is an interdisciplinary area that often takes advantage of tools from other fields including complex analysis and representation theory.

If you have any questions about the project, feel free to contact me at [email protected]

Amount

• Fully-paid tuition fees for four years at the home fee status.
• A tax-free bursary for living costs for four years (£18,622 per annum in 2023/24).
• Additional financial support is provided to cover short-term and long-term travel.
• If you are not a UK national, nor an EU national with UK settled/pre-settled status, you will need to apply for a student study visa before admission.

Eligibility

Applicants must hold, or expect to hold, at least a UK upper second class degree (or non-UK equivalent qualification) in Mathematics, or a closely-related area, or else a lower second class degree followed by a relevant Master's degree.

This award is open to UK and International students

Deadline: Friday 26th April 2024

How to apply

Apply through the University of Sussex on-line system. 

Select the PhD in Mathematics, with an entry date of September 2024.

In the Finance & Fees section, state that you wish to be considered for studentship number: RS/Math/01

We advise early application as the position will be filled as soon as a suitable applicant can be found.

Due to the high volume of applications received, you may only hear from us if your application is successful.

Contact us

If you have practical questions about the progress of your on-line application or your eligibility, contact [email protected] . For academic questions about the project, contact Dr Nick Simm at [email protected]