Mirror symmetry for fibrations and degenerations of Calabi-Yau manifolds
Loughborough UniversityLoughborough, United Kingdom
Course overview
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
Key highlights
- Research into mirror symmetry for Calabi-Yau manifolds using algebraic geometry
- Investigates conjectured mirror relationship between fibrations and degenerations
- Join a Geometry and Mathematical Physics group of 12 permanent staff
- Weekly research seminars and weekly student–supervisor meetings
- Strong links with research groups at neighbouring institutions
- 94% of research impact rated world-leading or internationally excellent (REF 2021)
Entry requirements
- Degree: 2:1 — or above
Scholarships
Alumni Bursary
10% of tuition fees which will be credited to the student’s tuition fee account.
Up to 10% of feesAlumni Discount
UK students: £1,500 tuition fee discount for one academic year. International students: £3,000 tuition fee discount for one academic year.
Care Leaver's Scholarship
Excellence Scholarships
UK students: £3,000 off tuition fees; International students: £6,000 off tuition fees which will be credited to the student’s tuition fee account.
International Sports Student Postgraduate Bursary
Our International Sports Student Postgraduate Bursary offers a £12,000 tuition fee discount (set against the tuition fees of your chosen postgraduate taught programme ONLY).
Up to £12,000London 10th Anniversary Award
£5,000 off tuition fees.
Up to £5,000Loughborough Business School Scholarship
£1,500 (UK students) and £3,000 (international students) off tuition fees which will be credited to the student’s tuition fee account.
MBA Progress with Purpose Scholarship
50% of tuition fees which will be credited to the student’s tuition fee account.
Up to 50% of feesQatari Ghanim Al-Muftah Excellence Scholarship
Careers this course leads to
- Postdoctoral research associate in mathematics
- University lecturer in pure mathematics
- Mathematical physicist
- Quantitative analyst
- Data scientist
Cost of study
UK/Home: £5,238 | International: £23,100
Admission
Applications are made through AHZ at no cost. Share your transcripts, English test scores and personal statement, and your AHZ Counsellor will review your profile, submit your application to Loughborough University, and guide you through interview, offer, CAS and visa — right up to enrolment.
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