Automorphic Lie Algebras associated to exceptional Lie algebras PhD

Department(s):
Mathematical Sciences
Entry requirements:
2:1+
Full-time:
3 years
Part-time:
not available
Reference number:
SL/MA/2018GT
Start date:
01 October 2018
Is funding available?
Yes
UK/EU fees:
N/A
International fees:
TBC
Location:
Loughborough
Application deadline:
16 February 2018

Achievements

87%

of research classed as 'internationally recognised'

REF 2014

21st

in the UK for Mathematics

The Complete University Guide 2018

Overview

Loughborough University is a top-ten rated university in England for research intensity (REF2014) and an outstanding 66% of the work of Loughborough’s academic staff who were eligible to be submitted to the REF was judged as ‘world-leading’ or ‘internationally excellent’, compared to a national average figure of 43%.

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. 

Project detail

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.

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.

Supervisors

Primary supervisor: Sara Lombardo

Find out more

For further project details email Sara Lombardo or register your interest and ask us a question.

To find out more about postgraduate research in the School of Science please visit our website.

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.

Applicants must meet the minimum English Language requirements, details available on the website.

Fees and funding

UK/EU:
N/A
International:
TBC

Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Special arrangements are made for payments by part-time students.

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.

How to apply

All applications should be made online. Under programme name, select ‘Mathematics’.

Please quote reference number: SL/MA/2018

Application details

Reference number:  SL/MA/2018
Start date: 01 October 2018
Application deadline: 16 February 2018

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