Funded PhD Studentship in Algebra

Summary

Research covers key areas of algebra, geometry, mathematical physics and topology. This reaches from the study of algebras, group theory (including Lie groups/algebraic groups), Lie algebras, Hopf algebras, (higher) category theory, representation theory and homological algebra to algebraic geometry, differential and difference equations, braid groups, configuration spaces, surfaces and manifolds, and to mathematics on the interface of algebra with topology and mathematical physics, such as the pentagon equation, skew braces, (extended) topological quantum field theories, higher Lie and gauge theory, mathematical models for topological phases of matter and the ensuing paradigms for topological quantum computing. There are also strong connections to Logic, where topics such as algebraic topology, category theory, categorical and homotopical algebra, model theory, permutation groups, surreal numbers and ordered fields play a role in the interface.

This is a strong and active area of research. There are many collaborations and interactions between researchers across these areas, both at Leeds and externally, and there is a thriving community of postdoctoral researchers (supported in part by a substantial EPSRC Programme Grant in combinatorial representation theory) and PhD students, as well as regular seminars in Algebra and in Mathematical Physics.

We are delighted to offer a fully funded PhD studentship and applications are invited from strongly motivated and academically excellent candidates for PhD study in Algebra, within these strategic priority Research areas:

Oleg Chalykh: Quivers and their representations; Moduli spaces in representation theory and mathematical physics; Cherednik algebras and double affine Hecke algebras. Please contact Dr Chalykh by email to o.chalykh@leeds.ac.uk

Ilaria Colazzo: Algebraic structures connected with combinatorial solutions of the Yang-Baxter equation and Pentagon equation. Please contact Dr Colazzo by email to I.Colazzo@leeds.ac.uk

Paul Martin: Algebras and computation for statistical mechanics; combinatorial and geometric algebra in the interface of mathematics with physics. Please contact Professor Martin by email to P.P.Martin@leeds.ac.uk

Joao Faria Martins: (Extended) topological quantum field theories; Hopf algebras and low dimensional topology; Algebraic models for homotopy types. Please contact Dr Faria Martins by email to J.FariaMartins@leeds.ac.uk

Rudolf Tange: Representations, invariants and actions of reductive algebraic groups in characteristic p. Please contact Dr Tange by email to R.H.Tange@leeds.ac.uk

Francesca Tripaldi: Spectral sequences on nilpotent Lie groups, homotopy transfer theorem on homogeneous Lie groups, Lie algebra cohomology of nilpotent Lie groups. Please contact Dr Tripaldi by email to F.Tripaldi@leeds.ac.uk

Michael Wibmer: Differential Galois theory; Difference algebraic groups. Please contact Dr Wibmer by email to M.Wibmer@leeds.ac.uk

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.