Mirror symmetry for fibrations and degenerations of Calabi-Yau manifolds (Ref: MA/AT-Un1/2025)

About the Project

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: a.m.thompson@lboro.ac.uk

Entry requirements

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.

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

Tuition fees for 2026-27 entry

• UK fee - £5,006 Full-time degree per annum
• International fee - £23,100 Full-time degree per annum

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.