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Birational Geometry of Singular Fano Varieties

  • Full or part time
  • Application Deadline
    Friday, February 14, 2020
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

About This PhD Project

Project Description

Application details:
Reference number: HA/MA/2020
Start date of studentship: 1 October 2020
Closing date of advert: 14 February 2020

Primary supervisor: Dr Hamid Ahmadinezhad
Secondary supervisor: To be decided
This studentship offers the chance to be a part of the dynamic group of algebraic geometry in Loughborough and to work with world-leading experts in birational geometry.
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.
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Loughborough University has a flexible working and maternity/parental leave policy ( and is a Stonewall Diversity Champion providing a supportive and inclusive environment for the LGBT+ community. The University is also a member of the Race Equality Charter which aims to improve the representation, progression and success of minority ethnic staff and students. The School of Science is a recipient of the Athena SWAN bronze award for gender equality.

Full Project Detail:
The project is about geometric objects called “Fano varieties”. The study of Fano varieties appears in many contexts in pure mathematics, with applications in Geometric Design, Theoretical Physics and beyond.
Geometric shapes defined by algebraic equations are called “varieties”. Familiar examples are the parabola (y=x2) and the sphere (x2+y2+z2=1). Sometimes two varieties can be identified after removing small subsets from them. For example, a sphere without its north pole can be projected to the 2-dimensional plane by a technique called stereographic projection. Identifications like this are called “birational maps”.
Knowing which varieties are birationally mapped into each other is a fundamental question in geometry. The main aim of this project is to study birational relations amongst Fano varieties that may have singular points.
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Entry requirements:
Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematics or a related subject. A relevant Master’s degree and/or experience in one or more of the following will be an advantage: Algebra, Algebraic Geometry, Differential Geometry, Computer Algebra.

Funding information:
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 3.5-year studentship provides a tax-free stipend of £15,009 (2019 rate) per annum for the duration of the studentship, plus tuition fees at the UK/EU rate. Due to funding restrictions, this is only available to those who are eligible to pay UK/EU fees. To qualify for a full award, all applicants must meet the EPSRC eligibility criteria including the minimum UK residency requirement:
Contact details:
Name: Dr Hamid Ahmadinezhad
Email address:
Telephone number: +44 (0)1509 222628

How to apply:

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

Please quote reference number: HA/MA/2020.

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