{"id":741,"date":"2025-10-09T09:13:21","date_gmt":"2025-10-09T09:13:21","guid":{"rendered":"https:\/\/scholarshipidea.net\/?p=741"},"modified":"2025-10-09T09:13:22","modified_gmt":"2025-10-09T09:13:22","slug":"phd-in-topological-and-geometric-properties-of-laplace-eigenfunctions-at-university-of-reading-uk","status":"publish","type":"post","link":"https:\/\/scholarshipidea.net\/?p=741","title":{"rendered":"PhD in Topological and Geometric Properties of Laplace eigenfunctions at University of Reading, UK"},"content":{"rendered":"\n
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Qualification Type:<\/th>PhD<\/td><\/tr>
Location:<\/th>Reading<\/td><\/tr>
Funding for:<\/th>UK Students<\/td><\/tr>
Funding amount:<\/th>\u00a320,780<\/td><\/tr>
Hours:<\/th>Full Time<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Placed On:<\/th>8th October 2025<\/td><\/tr>
Closes:<\/th>15th November 2025<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

<\/a><\/p>\n\n\n\n

Project title:<\/strong>  Topological and Geometric Properties of Laplace eigenfunctions<\/p>\n\n\n\n

Department\/School: SMPCS<\/strong><\/p>\n\n\n\n

Supervisors:  Sugata Mondal<\/strong><\/p>\n\n\n\n

Second advisor: Michael Levitin<\/strong><\/p>\n\n\n\n

Project Overview: <\/strong>Spectral geometryis 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 \u201cCan one hear the shape of a drum?\u201d<\/em> Explicit geometric invariants being the shape and the sound frequencies being the Laplace eigenvalues.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Our Community<\/strong><\/p>\n\n\n\n

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 \u2018outstanding\u2019 or \u2018very considerable\u2019 (Research Excellence Framework 2021, combining 4* and 3* submissions \u2013 Mathematical Sciences).    <\/p>\n\n\n\n

You will join a friendly, inclusive community of passionate staff and students in the Department of Mathematics and Statistics<\/a>, who will motivate you to achieve your goals and be part of the wider doctoral community at Reading.<\/p>\n\n\n\n

Eligibility: <\/strong><\/p>\n\n\n\n