Lieb-Thirring inequalities for Generalized Indefinite Strings (Ref: MA/JE-SF1/2026)

About the Project

Lieb-Thirring inequalities provide upper bounds on the negative eigenvalues of Schrödinger operators in terms of the potential. Such inequalities have important applications in quantum mechanics, in particular for establishing stability of matter. The aim of this project is to establish analogue inequalities for general second order ordinary differential equations (in the form of generalized indefinite strings and canonical systems). Work in this area will involve a combination of advanced tools in various areas of analysis.

Name of primary supervisor/CDT lead:
Jonathan Eckhardt J.Eckhardt@lboro.ac.uk

Entry requirements:
Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in a mathematics-related degree. The project also requires a good understanding of real, complex and functional analysis as well as measure theory.

English language requirements:
Applicants must meet the minimum English language requirements. Further details are available on the International website (http://www.lboro.ac.uk/international/applicants/english/).

Bench fees required: No

Closing date of advert: 1st February 2027

Start date: October 2026, February 2027, July 2027

Full-time/part-time availability: Full-time 3 years

Fee band: 2025/26 Band RA (UK £5,006, International £22,360)

How to apply:
All applications should be made online. Under programme name, select Mathematical Sciences. Please quote the advertised reference number: MA/JE-SF1/2026 in your application. To avoid delays in processing your application, please ensure that you submit a CV and the minimum supporting documents.

Project search terms:
Pure Mathematics, Analysis, Spectral Theory, Operator Theory

Email Address Sci:
sci-pgr@lboro.ac.uk