PhD Studentship: Automorphic Lie Algebras Associated to Exceptional Lie Algebras

Loughborough University

Start date of studentship: 1st October 2018

Supervisors:

Primary supervisor: Sara Lombardo

In Mathematics and Physics the concept of symmetry is fundamental, often associated with the idea of invariance. The research on Automorphic Lie Algebras ultimately aims to describe symmetries. If you enjoy linear and abstract algebra, and if you appreciate the elegance of analysis and group theory, this project is for you.

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/

Full Project Detail:

Symmetry has been a driving idea for art, architecture and music for centuries. Nature itself seems to be organised according to symmetries. In Mathematics and Physics the concept of symmetry plays a fundamental role, often associated with the idea of invariance (for example, under certain transformations). The research on Automorphic Lie Algebras (ALiAs) ultimately aims to describe symmetries. In fact, ALiAs could be described as continuous symmetries bearing a discrete symmetry themselves. More precisely, ALiAs are Lie algebras over a ring defined by invariance under the action of a finite group of automorphisms. They have been extensively studied in the last decade but only recently it was discovered that these algebras are intimately related with a cohomology theory on root systems.

In this project, you will have the opportunity to work with world-leading experts in the theory of Automorphic Lie Algebras. In particular, you will adopt the latest theory to classify ALiAs associated to exceptional simple Lie algebras, starting from g_2, the smallest exceptional simple Lie algebra. If you enjoy linear and abstract algebra, and if you appreciate the elegance of analysis and group theory, this project is for you. Some ability to program and/or use computer algebra systems (such as GAP, Mathematica, etc.) might be an advantage.

Find out more:

For potential implications and further information on the project see - http://www.lboro.ac.uk/science/study/postgraduate-research/studentships/

http://www.lboro.ac.uk/departments/maths/staff/academic/lombardosara/

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: Mathematics and/or Mathematical Physics.

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-year studentship provides a tax-free stipend of £14,553 (2017 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.

Contact details:

Name: Sara Lombardo

Email: s.lombardo@lboro.ac.uk

Tel: +44 (0) 1509-223327

How to apply:

Applications should be made online at http://www.lboro.ac.uk/study/apply/research/. Under programme name, select Mathematics.

Please quote reference number: SL/MA/2018

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Type / Role:

PhD

Location(s):

Midlands of England