PhD Studentship in “Applications of harmonic analysis in probability and equidistribution theory”

The Project

Classical Fourier analysis as well as abstract harmonic analysis on groups and manifolds provide powerful tools in a large number of areas including number theory, probability theory, equidistribution theory and optimal transport. The aim of the PhD project is to develop a flexible framework based on harmonic analysis to study random and deterministic systems and point configurations. Potential applications include number theoretic constructions such as lattices, dynamical systems, as well as random systems such as Poisson and determinantal point processes, eigenvalues of random matrices, and random walks on groups.

During the project you will learn how to apply harmonic analysis to the equidistribution theory of point configurations in various domains including the unit cube, the unit sphere, groups, manifolds and discrete spaces such as finite fields. You will learn about spectral methods in the theory of random walks and dynamical systems. Immediate applications include quadrature rules in numerical integration, energy minima of particle systems in physics, and cryptography.

You will work under the supervision of Dr Bence Borda. You will become a member of an active probability research group, which currently includes 6 faculty members, 2 postdocs and 4 PhD students. The research interests of the faculty include random trees and random graphs, random matrices, free probability, statistical mechanics, probabilistic number theory, random walks, Markov chains, stochastic geometry, interacting particle systems and large deviations.

The ideal candidate has a passion for mathematics and excellent communication skills. Students with an interest in at least one of the following areas are encouraged to apply:

• Classical or abstract harmonic analysis
• Probabilistic number theory
• Point processes and random walks

Amount

• Fully-paid tuition fees for three and a half years at the home fee status.
• A tax-free bursary for living costs for three and a half years (£19,237 per annum in 24/25).
• 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 else a lower second class degree followed by a relevant Master's degree.

This award is open to UK and International students

Deadline: 28 February 2025

How to apply

Apply through the University of Sussex on-line system, by clicking the 'Apply' button, above.

https://www.sussex.ac.uk/study/phd/apply/log-into-account

Select the PhD in Physics/Mathematics, with an entry date of September 2025.

In the Finance & Fees section, state that you wish to be considered for studentship no PS/2025/01

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 mps-pgrsupport@sussex.ac.uk

For academic questions about the project, contact Dr Bence Borda at b.borda@sussex.ac.uk

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