PhD Studentship: Topological and Geometric Properties of Laplace Eigenfunctions

PhD Studentship in Analysis of PDE 

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. 

The University of Reading is in the top 125 in the world for Physical Sciences (Times Higher Education World University Rankings 2024, by Subject). We have a long and established track record of research that makes an impact. 98% of our research is world leading or internationally excellent and 100% of our research impact has been classed ‘outstanding’ or ‘very considerable’ (Research Excellence Framework 2021, combining 4* and 3* submissions – Mathematical Sciences). 

When you start a PhD in mathematics at Reading, you'll join a friendly, inclusive community of passionate staff and students in the Department of Mathematics and Statistics, who will motivate you to achieve your goals. You'll also be part of the wider doctoral community at Reading. You can find out more information about the Department, its research and PhD provision on the Department of Mathematics and Statistics’ website. 

During your PhD at the University of Reading, you will expand your research knowledge and skills, receiving specialist supervision. You will also gain transferable skills that will support your career aspirations.

Eligibility: 

• Applicants should hold or expect to gain a minimum of a 2:1 (upper second class) bachelor's degree or equivalent in mathematics, and ideally in, or with a substantial component of pure mathematics.
• Due to the nature of the funding this studentship is open to UK/Republic of Ireland applicants.

Funding Details:   

• Starts September 2025
• 4-year award
• Funding covers UK/Republic of Ireland full tuition fees plus UKRI stipend (stipend for the 2025-26 academic year is £20,780)

How to apply:   

Please click on the ‘Apply’ button above to be redirected to our website “Apply for a Programme”, 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: 16 May 2025 

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

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. 

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