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
Country
United Kingdom
University
University of East Anglia
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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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