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University of East Anglia

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University of East Anglia PhD Studentship

PhD Studentship in Formalising the Local Langlands Correspondence for GL₂(F) in Lean University of East Anglia in United Kingdom

Degree Level

PhD

Field of study

Computer Science

Funding

The project is offered on a self-funded basis; no funding amount is specified. Applicants may be self-funded or seeking external funding. A bench fee is payable in addition to tuition fees for specialist equipment and laboratory facilities. Eligible University of East Anglia alumni may receive a tuition fee discount.

Deadline

Nov 30, 2026

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Country

United Kingdom

University

University of East Anglia

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Keywords

Computer Science
Mathematics
Number Theory
Harmonic Analysis
Representation Theory

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About this position

The University of East Anglia is offering a PhD project at its Norwich campus on formalising the local Langlands correspondence for GL₂(F) in the Lean interactive theorem prover. The research sits at the intersection of number theory, representation theory, formal mathematics, and computer-verified proof.

The project will begin by formalising the sophisticated mathematical structures needed to state the local Langlands correspondence. One part will address the representation theory of GL₂(F), where F is a non-Archimedean local field, including irreducible admissible representations. The other will develop the theory of two-dimensional Galois representations of the Weil group of F.

A second phase will establish a framework for formalising the proof itself. The student will use Lean and AI agents to create a computer-verified library and lay the foundations for a long-term verification programme in contemporary mathematics. The work connects harmonic analysis with number theory through one of the central correspondences of the modern Langlands programme.

The project is supervised by Dr. Christopher Birkbeck at the University of East Anglia, providing a research environment focused on advanced mathematical formalisation and interactive theorem proving.

Funding details

The project is offered on a self-funded basis; no funding amount is specified. Applicants may be self-funded or seeking external funding. A bench fee is payable in addition to tuition fees for specialist equipment and laboratory facilities. Eligible University of East Anglia alumni may receive a tuition fee discount.

What's required

Applicants must have at least a 2:1 Bachelor's degree and a Master's degree in mathematics. The project is available for full-time or part-time study, and applicants must be self-funded or be in the process of securing external funding.

How to apply

Review the project details and apply through the jobs.ac.uk advert or University of East Anglia doctoral application process. Applicants should contact Dr. Christopher Birkbeck for details of the applicable bench fee and funding information.

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