Job Description
Project details
The number of negative eigenvalues of a Schrödinger operator in the asymptotic regime of large coupling is given by the celebrated Weyl law. A textbook proof of the leading order term in Weyl’s law uses coherent states – states that are as well-localized in phase-space as permitted by the Heisenberg uncertainty principle. This project aims to use coherent state methods (closely related to the so-called FBI transform) to go beyond leading order. Although these results can be obtained by highly sophisticated techniques such as Fourier Integral Operator calculus, coherent states offer a very flexible and robust alternative and are physically well-motivated.
94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021
Supervisors
Primary supervisor: Jean-Claude Cuenin
Entry requirements
Our entry requirements are listed using standard UK undergraduate degree classifications i.e. first-class honours, upper second-class honours and lower second-class honours. To learn the equivalent for your country, please choose it from the drop-down below.
Entry requirements for United Kingdom
Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in a mathematics related degree. A solid grasp of real and functional analysis and some basic knowledge of PDE and / or quantum mechanics.
English language requirements
Applicants must meet the minimum English language requirements. Further details are available on the International website.
Applicants must meet the minimum English language requirements. Further details are available on the International website.
Fees and funding
Tuition fees for 2025-26 entry
UK fee
£5,006 Full-time degree per annum
International fee
£22,360 Full-time degree per annum
Fees for the 2025-26 academic year apply to projects starting in October 2025, January 2026, April 2026 and July 2026.
Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Fees are reviewed annually and are likely to increase to take into account inflationary pressures.
How to apply
All applications should be made online. Under programme name, select School of Science/Mathematical Sciences. Please quote reference number: MA/J-CC-SF1/2025 in your application.
To avoid delays in processing your application, please ensure that you submit a CV and the minimum supporting documents.
The following selection criteria will be used by academic schools to help them make a decision on your application. Please note that this criteria is used for both funded and self-funded projects.
Please note, applications for this project are considered on an ongoing basis once submitted and the project may be withdrawn prior to the application deadline, if a suitable candidate is chosen for the project.
