Congratulations to Abhishek Saha whose research grant proposal 'New investigations in automorphic forms: analytic and arithmetic interfaces' has been awarded funding by the Leverhulme Trust worth £293,685.
To what degree of accuracy can we predict the number of primes in an interval? How high are the peaks of the vibration modes on a negatively curved membrane? Does a quantum particle moving freely on a space get equally distributed everywhere as its energy increases?
This project will study higher-dimensional analogues of the above questions. These questions and their generalisations are all connected together by the notion of an automorphic form: automorphic forms are highly symmetric functions that constitute one of the most important concepts in modern mathematics. They were key to solving many longstanding problems, such as Fermat’s Last Theorem and the hypersphere-packing problem.
In a significant departure from existing work in this field, this project will approach the deepest problems in automorphic forms simultaneously from the analytic, algebraic, and arithmetic directions, with representation theory as the crucial unifying glue. The methodologies and techniques developed over the course of this project will have applications to a number of problems across mathematics and physics.
This Leverhulme Trust research project grant will fund a one year fixed-term replacement lecturer, a postdoctoral researcher for 3 years and a PhD student.