PhD-Mirror symmetry for fibrations and degenerations of Calabi-Yau manifolds
PhD @Loughborough University posted 14 hours agoJob Description
Project details
Calabi-Yau manifolds are an important class of objects in algebraic geometry, yet many of their properties are still poorly understood. Evidence from theoretical physics, and in particular string theory, suggests that Calabi-Yau manifolds seem to come in pairs, with related properties. This observed phenomenon is called mirror symmetry. However, whilst we now have thousands of examples of such “mirror pairs” of Calabi-Yau manifolds, there is still no underlying mathematical theory to explain how and why they arise.
This project aims to use algebraic geometry to study the relationship between “fibrations” on a Calabi-Yau manifold and “degenerations” of its mirror partner. Fibrations can be thought of as ways to slice a Calabi-Yau manifold into thin slices, whilst degenerations can be thought of as ways to bend a Calabi-Yau manifold until it breaks into smaller pieces. It is conjectured that fibrations and degenerations are mirror to one another; this project aims to gather evidence for such a conjecture.
The successful applicant will join the Geometry and Mathematical Physics Research Group, which currently includes 12 permanent academic staff along with several research associates and PhD students. The group has a vibrant research culture, with activities including weekly research seminars, weekly meetings between students and supervisors, and excellent links with groups in neighbouring institutions.
94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021
Supervisors
Primary supervisor:Â Dr Alan Thompson
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.
Entry requirements for United Kingdom
Applicants should have, or expect to achieve, at least a 2:1 Honours degree at Master’s level in mathematics (or equivalent). Candidates should be hardworking, good at communicating, and able to work both independently and as part of a team.
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 2024-25 entry
UK fee
£4,786 Full-time degree per annum
International fee
£21,500 Full-time degree per annum
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 2024-25 academic year apply to projects starting in October 2024, January 2025, April 2025 and July 2025.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 Mathematical Sciences. Please quote the advertised reference number: MA/AT-Un1/2025 in your application.
To avoid delays in processing your application, please ensure that you submit 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, 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.
