拉夫堡大学数学科学系招收博士研究生
Project
Eigenvalues of functional difference operators associated to mirror curves
About the Project
Toric Calabi–Yau manifolds play an important role in mathematical physics. Their mirror manifolds can be described by algebraic curves and recently it was observed that quantisation of these curves leads to functional-difference operators. The eigenvalues of these operators are conjectured to relate to geometric properties of the associated Calabi–Yau manifolds.
Formally, the operators are differential operators of infinite order. Studying properties of their eigenvalues is thus of twofold importance. Firstly, it sheds more light on the conjectured connection to Calabi–Yau manifolds. Secondly, any results obtained can be expected to form limit cases in known spectral results for finite-order differential operators.
This project will build on recent progress in establishing eigenvalue bounds for some of these operators. Specifically, it will investigate the asymptotic behaviour of the eigenvalues. Due to the peculiar nature of these operators, several concepts that are well known for finite-order differential operators cannot be directly applied and will need to be modified.
The successful candidate will be part of the Analysis and PDE group at Loughborough University, benefitting from a stimulating environment that includes weekly research seminars, diverse expertise in spectral theory and mathematical physics, as well as links with research groups across the UK and EU. The university provides supportive and flexible working arrangements. It is a member of the Race Equality Charter, a Disability Confident Leader and a Stonewall Diversity Champion. The School of Science holds an Athena SWAN bronze award for gender equality.
Supervisors
Dr Lukas Schimmer - l.schimmer@lboro.ac.uk
Entry requirements for United Kingdom
Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in mathematics or physics. A relevant Master’s degree and/or a strong background in analysis are of advantage.
English language requirements
Applicants must meet the minimum English language requirements. Further details are available on the International website.
Find out more about research degree funding
How to apply
All applications should be made online. Under programme name, select Mathematical Sciences. Please quote the advertised reference number MA/LS-Un1/2023 in your application.
To avoid delays in processing your application, please ensure that you submit the minimum supporting documents.
Funding Notes
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.
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