At a Glance
- Tasks: Explore number theory and AI to formalise the Langlands program and develop new mathematical insights.
- Company: University of East Anglia, known for innovative research and academic excellence.
- Benefits: Fully funded PhD with a competitive stipend, tuition coverage, and research support.
- Other info: Dynamic research environment with opportunities for original contributions and career development.
- Why this job: Join a cutting-edge project that merges AI with mathematics and contributes to groundbreaking research.
- Qualifications: Minimum 2:1 in Mathematics required; passion for number theory and AI is essential.
The predicted salary is between 63000 - 77000 £ per year.
This fully funded PhD project, based at our Norwich campus, offers an opportunity to work at the intersection of number theory, artificial intelligence and formal mathematics. You will investigate how AI can help us formalise and deepen our understanding of the Langlands program, with the aim of producing new mathematical insights, proving new results and strengthening existing ones.
A concrete starting point will be the local Langlands correspondence for GL2(F) where F is a non-Archimedean local field. This correspondence provides a deep bridge between harmonic analysis and number theory, relating irreducible admissible representations of GL2(F) to two-dimensional Weil–Deligne representations. Using AI tools alongside the Lean 4 proof assistant, you will work towards formalising this correspondence, developing computer-verified definitions and theorems on both sides and progressing towards its construction and proof.
You will have access to leading AI tools to support both formalisation and mathematical exploration. You will investigate how these tools can help you understand difficult arguments, work through examples, formulate conjectures, explore proof strategies and develop formally verified proofs. A central theme will be the interaction between mathematical understanding and formalisation: using the process of making definitions and arguments precise to clarify existing mathematics and motivate new research questions.
The project is not limited to verifying known results. Alongside the formalisation effort, you will use AI to explore questions within the wider Langlands programme, seeking opportunities to establish new theorems and insights, extend or sharpen existing results, and find simpler or more conceptual proofs. These investigations will develop together with the formal work, with insights from each helping to guide the other.
The ambition is to produce both reusable, computer-verified mathematics and original contributions to number theory, while developing effective ways to combine AI-assisted exploration with rigorous mathematical proof.
Entry Requirements: The minimum entry requirement is 2:1 in Mathematics.
Mode of Study: Full-Time
Start date: 1 October 2027
Additional Funding Information: This four-year funded studentship, starting in October 2027, comprises tuition fees at Home fee rate, an annual tax-free stipend at the UEA rate (£20,409 in 2026/27, subject to any agreed inflationary uplift for 2027/28), and a Research Training Support Grant of £3,000 per annum. It is open to applicants eligible for Home fee status.
PhD Studentship: Studying the Langlands program via formalisation and AI in Norwich employer: University of East Anglia
The University of East Anglia (UEA) is an exceptional employer, offering a supportive work culture that prioritises employee growth and development. As a Commercialisation Administrator, you will benefit from a generous benefits package, including 34 days of annual leave, and the opportunity to contribute to meaningful projects that impact society and the economy. UEA's commitment to gender equality, recognised by its Athena Swan Silver Institutional Award, further enhances its reputation as a progressive workplace.
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We think this is how you could land PhD Studentship: Studying the Langlands program via formalisation and AI in Norwich
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Discuss Your Future Research Goals:In your motivation section, it’s a great idea to talk about your future research goals and how they align with the work being done at University of East Anglia. This shows that you’re not just looking for any job, but rather a chance to contribute meaningfully to the field. We love to see applicants who are forward-thinking and enthusiastic about their research journey!
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