Topological and Geometric Properties of Laplace eigenfunctions

Spectral geometry is the area of mathematics where one studies inter-relations between explicit geometric invariants of a Riemannian (or sub-Riemannian) manifold with the spectrum of the Laplace (or Laplace type) operators. The motivation comes from the famous question of M. Kac “Can one hear the shape of a drum?” Explicit geometric invariants being the shape and the sound being the Laplace eigenvalues.

This project will mostly concern the eigenfunctions of the Laplace operator. These functions exhibit various interesting topological and geometric properties. For example, harmonic functions on any domain achieve their maximum/minimum values only on the boundary of the domain. This project will delve into topological and geometric properties of eigenfunctions when their eigenvalues are not large.

Eligibility: Applicants should hold or expect to gain a minimum of a 2:1 bachelor’s degree or equivalent in Pure Mathematics.

Due to restrictions on the funding this studentship is open to UK applicants only.

Further enquiries contact: s.mondal@reading.ac.uk