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Calabi-Yau manifolds: families, fibrations, and degenerations


Project Description

The Department of Mathematical Sciences at Loughborough University seeks a qualified candidate for a PhD studentship in algebraic geometry. Algebraic geometry is a vibrant, growing field that has deep links to many other parts of pure mathematics, including number theory, analysis, and topology. The proposed project is motivated by recent ideas in mirror symmetry, which lies on the interface of algebraic geometry, mathematical physics, and string theory; the successful candidate will have the potential to contribute to significant new developments in this field.

Loughborough University is a top-ten rated university in England for research intensity (REF2014). In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career.

Find out more: http://www.lboro.ac.uk/study/postgraduate/supporting-you/research/
For further information on the Department of Mathematical Sciences see - https://www.lboro.ac.uk/departments/maths/research/

Full Project Detail

The successful candidate will work on a project to investigate the properties of a certain type of manifold, called a “Calabi-Yau manifold”. The special properties of Calabi-Yau manifolds mean that they appear in many areas of pure mathematics, from a central position in classification problems in algebraic geometry, to the use of 1-dimensional Calabi-Yau manifolds (a.k.a. elliptic curves) in number theory, and the special role played by 3-dimensional Calabi-Yau manifolds in mathematical physics and string theory.

The proposed project involves the construction and study of Calabi-Yau manifolds using two main techniques: “fibrations” and “degenerations”. Both methods involve studying the Calabi-Yau manifold by breaking it up into simpler pieces, but the ways in which they do this are very different. Fascinatingly there seems to be a deep link between the two approaches, through the mathematics of mirror symmetry, but this relationship is still very poorly understood. A large portion of the project will involve the investigation of this link.

Find out more:
http://www.lboro.ac.uk/science/study/postgraduate-research/studentships/

Entry requirements

Applicants should have, or expect to achieve, at least a 2:1 Honours degree at Master’s level in mathematics (or equivalent). Knowledge of abstract algebra and complex analysis is essential; some prior experience of algebraic geometry would be advantageous.

How to apply

All applications should be made online at http://www.lboro.ac.uk/study/apply/research/. Under programme name, select ‘Mathematical Sciences’.

Please quote reference number: AT/MA/2019.

Funding Notes

This studentship will be awarded on a competitive basis to applicants who have applied to this project and/or any of the advertised projects prioritised for funding by the School of Science.

The 3-year studentship provides a tax-free stipend of £14,777 (2018 rate) per annum (in line with the standard research council rates) for the duration of the studentship plus tuition fees at the UK/EU rate. International (non-EU) students may apply however the total value of the studentship will be used towards the cost of the International tuition fee in the first instance.

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