Dr D Stewart
No more applications being accepted
Competition Funded PhD Project (Students Worldwide)
About the Project
In the early part of the 20th Century, the simple Lie algebras over the complex numbers were classified by Killing and Cartan. These are algebraic structures which arise by differentiating the action of smooth groups of symmetries, called Lie groups. It turns out that each of the simple Lie algebras found can be defined over the integers; thus they are defined for any ring, and in particular, any field of any positive characteristic. Lie algebras over such fields are called modular Lie algebras. It turns out that for algebraically closed fields one can again classify the simple Lie algebras, a programme completed by Premet—Strade in 2006. (There are many more isomorphism types than over the complex numbers.)
The next step is to understand these algebras better; for example, their representation theory and their subalgebra structure. A particularly important idea connecting these two areas is that of G-complete reducibility. This was originated by Serre in the context of spherical buildings and algebraic groups, but similar notions exist for Lie algebras. In a recent paper with Adam Thomas, I found tight bounds on the characteristic of the field which would permit non-G-completely reducible simple subalgebras to exist in classical Lie algebras. As part of this project, one could go further, classifying the conjugacy classes of non-G-cr subalgebras in classical Lie algebras and considering analogous ideas for the Lie algebras of Cartan type.
It should be noted, that successful applicants will also be given the opportunity to complete teaching and demonstrating duties within the school amounting to up to £1500 per annum.
Funding Notes
This studentships is available to UK/EU and International candidates, who have/expect a 2:1 honours degree in computing science, mathematics, physics, statistics or another strongly quantitative discipline, or an international equivalent.
Applicants whose first language is not English require a minimum of IELTS 6.5. International applicants may require an ATAS (Academic Technology Approval Scheme) clearance certificate prior to obtaining their visa and to study on this programme.
The studentship includes tuition fees, a tax-free stipend of (up to) £14,296pa (16/17 level), a desktop computer, and £1500 travel allowance.