PhD Studentship in Analysis of PDE: Topological and Geometric Properties of Laplace Eigenfunctions

Supervisors: Sugata Mondal

Second advisor: Michael Levitin

Project Overview: 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.

Funding Details:   

• Starts September 2025
• 4-year award
• Funding covers full tuition fees plus UKRI stipend (Current stipend for the 2024-25 academic year is £19,237) 

How to apply:   

Apply online via the above ‘Apply’ button, create your account, and use the link sent by email to start the application process. During the application process please select the PhD in Mathematics (Pure Mathematics)

*Important notes*

1. Please quote the reference ‘DRC25-007’ in the ‘Scholarships applied for’ box which appears within the Funding Section of your on-line application.
2. If the application system prompts you to submit a research proposal, please paste in the project title and move on to the next step in the application.

Application Deadline: 28 February 2025

Further Enquiries:  

Please note that, where a candidate is successful in being awarded funding, this will be confirmed via a formal studentship award letter; this will be provided separately from any Offer of Admission and will be subject to standard checks for eligibility and other criteria. 

For further details please contact Dr. Sugata Mondal email: s.mondal@reading.ac.uk

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