PhD Studentship: Arithmetic Moments and Random Matrix Statistics over Function Fields

Overview

The University of Exeter, specifically within the Department of Mathematics and Statistics, offers a PhD studentship focused on arithmetic moments and random matrix statistics over function fields. The research centers on analytic number theory, function-field arithmetic, and random matrix theory across three interlinked strands. These include investigating moments of L-functions at s equals 1 for quadratic Dirichlet characters, studying shifted correlation sums for the k fold divisor function, and exploring moments of moments of characteristic polynomials for random matrices drawn from classical groups. The project also provides scope for utilizing AI-assisted methods such as symbolic computation and machine learning for conjecture generation and numerical verification alongside classical techniques. The outlined research strands serve as general guidance and allow flexibility for other topics within the field to be selected based on the candidate's background and interests.

What you get

The funding for this studentship covers tuition fees and provides an annual stipend of £21,805 for the 2026/7 period. The successful candidate will receive training in at least one area encompassing analytic number theory, function-field arithmetic, and random matrix theory.

Key dates

The closing date for applications is 2026-12-08.