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Birational geometry of Calabi--Yau varieties

Department of Mathematics

About the Project

This project is in algebraic geometry, a thriving research area at the heart of modern mathematics. The successful applicant will investigate the geometry of Calabi--Yau varieties --- geometric objects of central importance, both in algebraic geometry itself and in related areas such as differential geometry and high-enrgy physics. Theoretical understanding of Calabi--Yau varieties remains very incomplete, but in recent years exciting progress has been made in generating extensive databases of examples of Calabi--Yau varieties in dimensions 3 and 4. These databases will provide a rich testing ground in which to develop our understanding.

A major focus of the project will be the Morrison--Kawamata conjecture, an important open problem in the field that aims to describe the geometry of algebraic varieties in a uniform way. The student will develop effective methods to verify the conjecture for large families of Calabi--Yau varieties from the databases described above. Successful progress will require the student to use a combination of explicit computational methods together with powerful tools from birational geometry. The project has scope for expansion in several directions, for example the development of a more theoretical approach to the conjecture for Calabi--Yaus.

The successful applicant will join the Centre for Geometry and Applications at Loughborough. Established in 2017, this Centre supports research in geometry and related areas such as mathematical physics. At present there are 8 permanent academic staff, together with a growing group of postdoctoral and PhD researchers. The Centre has a vibrant research culture, with activities include weekly research seminar, regular meetings, and excellent links with groups in neighbouring institutions.

Entry requirements

Students should have, or expect to achieve, at least a 2:1 or equivalent degree classification in mathematics.

How to apply

All applications should be made online at Under programme name, select “Mathematical Sciences”.

Please quote reference number: MA/APS-Un1/2021

Start dates: April 2021, July 2021, October 2021

Duration: Full-time (3 years)

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