PhD Studentship in Analysis of PDE

Project title:  Topological and Geometric Properties of Laplace eigenfunctions

Department/School: SMPCS

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 frequencies being the Laplace eigenvalues.

This project will revolve around various questions in spectral geometry, especially around low eigenvalues and related eigenfunctions. The eigenfunctions exhibit various interesting topological and geometric properties and are intimately related to the geometry of the underlying manifold. The project will focus on understanding various aspects of these properties and using them to answer quantitative (counting problems) and qualitative (structure of level sets) questions in spectral geometry.

Our Community

You will be joining an outstanding, impactful department of mathematics and statistics. 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).    

You will 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 and be part of the wider doctoral community at Reading.

Eligibility: 

• Applicants should hold or expect to gain a minimum of a 2:1 bachelor's degree or equivalent in pure mathematics.
• Due the nature of the funding this studentship is open to UK/Republic of Ireland applicants only.

Funding Details:   

• Starts September 2026
• 4-year award
• Funding covers full tuition fees plus UKRI stipend (£20,780 for 2025/26)

How to apply:  

To apply click the 'Apply' button above, 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.

*Important notes*

• 1) Please quote the reference ‘GS26-001’ 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: 15 November 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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