Formalising the Local Langlands Correspondence for GL₂(F) in Lean (BIRKBECKC_U26EMP)

This self-funded PhD project, based at our Norwich campus, offers a unique opportunity to work at the confluence of number theory, representation theory, and formal mathematics. You will undertake a single, ambitious research project: to begin the formalisation of the local Langlands correspondence for GL2(F) in the Lean interactive theorem prover. This correspondence is a cornerstone of the modern Langlands program, providing a deep and unforeseen bridge between harmonic analysis and number theory.The primary goal of this project is to formalise the sophisticated mathematical objects required to state the main theorem.

This will involve developing a computer-verified library for the two sides of the correspondence:1. The representation theory of GL2(F), where F is a non-Archimedean local field, including the theory of irreducible admissible representations.2. The intricate structure of two-dimensional Galois representations of the Weil group of F.Once the definitions are in place, the second phase of the project will be to create a comprehensive framework to guide the formalisation of the proof itself, laying the groundwork for a long-term verification effort.

This foundational work will be a landmark achievement in the digital formalisation of contemporary mathematics. The standard minimum entry requirement is 2:1 in Mathematics. This project is offered on a self-funding basis.

It is open to applicants with funding or those applying to funding sources. Details of tu