Outline

The research interests of the Mathematics Group cover a wide range of topics following our strategy of cohesion with diversity. Areas of interest include nonlinear equations, the Painleveé equations, classification of integrable systems, geometric integration, quantum integrable systems and topological solutions, functional analysis, representation theory and invariant theory of finite groups, non-commutative geometry, and computational commutative algebra.

Programme structure

For further information see the School site.

Funding

Every school at Kent offers one or two University postgraduate research scholarships, each available for three years, providing fees at the home/EU rate and a stipend up to £13,590 per annum (2011/12 rate). Many schools offer scholarships in the form of Graduate Teaching Assistantships (GTAs) whereby postgraduate research students receive financial support in return for teaching. The value of awards may vary, but often cover tuition fees at the home/EU rate and a substantial maintenance grant. All postgraduate research students are eligible to apply for GTAs. See Graduate Teaching Assistantships.
We are one of 35 mathematics departments awarded an EPSRC doctoral training account to fund research students. In 2010, we received a significant increase in EPSRC funding. Occasionally, EPSRC project studentships become available and are advertised on our web pages.
The School has established a bursary scheme to support students who wish to study on the Mathematics and its Applications MSc programme.
The School will award bursaries between £500 and £1,500. All applicants who accept a place on the above course will automatically be considered for a bursary. Overseas and home/EU fee-paying students are all eligible. There is no formal closing date, but we recommend you apply for your chosen programme before the end of July 2012.
For further details of postgraduate funding, see Postgraduate funding.

Further information:

• Scholarships website
• Funding website
• Finance Office

Resources and facilities

The University's Templeman Library houses a comprehensive collection of books and research periodicals. Online access to a wide variety of journals is available through services such as Science Direct and SpringerLink. The School has licences for major numerical and computer algebra software packages. Postgraduates are provided with computers in shared offices in the School.

Further information:

• School website
• Canterbury campus

Research areas

Areas of interest include nonlinear differential equations, the Painlevé equations, classification of integrable systems, geometric integration, quantum integrable systems and topological solitons, functional analysis, representation theory and invariant theory of finite groups, non-commutative geometry, and computational commutative algebra.

The research on nonlinear differential equations primarily studies algorithms for their classification, normal forms, symmetry reductions and exact solutions. Boundary value problems are studied from an analytical viewpoint, using functional analysis and spectral theory to investigate properties of solutions. We also study applications of symmetry methods to numerical schemes, in particular the applications of moving frames.

Current research on the Painlevé equations involves the structure of hierarchies of rational, algebraic and special function families of exact solutions, Bäcklund transformations and connection formulae using the isomonodromic deformation method. The group is also studying analogous results for the discrete Painlevé equations, which are nonlinear difference equations.

Artificial immune systems use nonlinear interactions between cell populations in the immune system as the inspiration for new computer algorithms. We are using techniques of nonlinear dynamical systems to analyse the properties of these systems.

Current research on quantum integrable systems focuses on powerful exact analytical and numerical techniques, with applications in particle physics, quantum information theory and mathematical physics.

Topological solitons are stable, finite energy, particle-like solutions of nonlinear wave equations that arise due to the general topological properties of the nonlinear system concerned. Examples include monopoles, skyrmions and vortices.
This research focuses on classical and quantum behaviour of solitons with applications in various areas of physics including particle, nuclear and condensed matter physics. The group employs a wide range of different techniques including numerical simulations, exact analytic solutions and geometrical methods.

A representation of a group is the concrete realisation of the group as a group of transformations. Representation theory played an important role in the proof of the classification of finite simple groups, one of the outstanding achievements of 20th-century algebra.

Representations of both groups and algebras are important in diverse areas of mathematics, such as statistical mechanics, knot theory and combinatorics.

Invariant theory has its roots in the classical constructive algebra of the 19th century and motivated the development of modern algebra by Hilbert, Noether, Weyl and others. There are natural applications and interactions with algebraic geometry, algebraic topology and representation theory. The starting point is an action of a group on a commutative ring, often a ring of polynomials on several variables. The ring of invariants, the subring of fixed points, is the primary object of study.

We use computational methods to construct generators for the ring of invariants, and theoretical methods to understand the relationship between the structure of the ring of invariants and the underlying representation.

Staff research

Professor Peter A Clarkson: Professor of Mathematics
Symmetry reductions and exact solutions of nonlinear partial differential equations; reductions of the self-dual Yang-Mills equations; soliton theory and discrete and continuous Painlevé equations.

Dr Clare Dunning: Senior Lecturer in Applied Mathematics
Exactly solvable models in mathematical physics; integrable quantum field theory and spectral theory of ordinary differential equations.

Professor Peter Fleischmann: Professor of Pure Mathematics
Representation theory and structure theory of finite groups; constructive invariant theory; applied algebra and discrete mathematics.

Professor Andrew Hone: Professor of Mathematics
Nonlinear dynamical systems; coherent structures in nonlinear differential equations, particularly solitons in integrable systems; Painlevé transcendents; exactly solvable models of mathematical physics and mathematical biology.

Dr Steffen Krusch: Lecturer in Applied Mathematics
Topological solitons in mathematical physics, in particular the classical and quantum behaviour of skyrmions.

Dr Stéphane Launois: Senior Lecturer in Pure Mathematics
Non-commutative algebra and non-commutative geometry, in particular, quantum algebras and links with their (semi-)classical counterparts: enveloping algebras and Poisson algebras.

Dr Bas Lemmens: Lecturer in Mathematics
Analysis, metric geometry and combinatorics; applications in optimal control, game theory and computer science.

Professor Elizabeth L Mansfield: Professor of Mathematics
Nonlinear differential and difference equations; variational methods; moving frames and geometric integration.

Dr Rowena Paget: Lecturer in Pure Mathematics
Representation theory of groups and algebras, with emphasis on algebras possessing a quasihereditary or cellular structure, such as the group algebras of symmetric groups, Brauer algebras and other diagram algebras.

Dr Markus Rosenkranz: Lecturer in Mathematics
Symbolic methods for (linear) boundary problems; computer algebra; differential algebra; D-module theory.

Dr R James Shank: Reader in Mathematics
The invariant theory of finite groups and related aspects of commutative algebra; algebraic topology and representation theory.

Dr Jing Ping Wang: Lecturer in Applied Mathematics
Geometric and algebraic properties of nonlinear partial differential equations; test and classification of integral systems and asymptotic normal forms of partial differential equations.

Dr Ian Wood: Lecturer in Mathematics
Analysis of PDEs and spectral theory, in particular, the study of spectral properties of non-self adjoint operators via boundary triples and M-functions (generalised Dirichlet-to-Neumann maps), regularity to solutions of PDEs in Lipschitz domains and waveguides in periodic structures.

Dr Chris Woodcock: Senior Lecturer in Pure Mathematics
P-adic analogues of classical functions; commutative algebra; algebraic geometry; modular invariant theory.

Further information:

• School website
• School staff profiles

Contact details

Admissions enquiries
T: +44 (0)1227 827272
E: information@kent.ac.uk
Subject enquiries

Mathematics Postgraduate Admissions Officer
School of Mathematics, Statistics and Actuarial Science,
Cornwallis Building,
University of Kent, Canterbury, Kent CT2 7NF, UK
T: +44 (0)1227 827181
E: imspg-admiss@kent.ac.uk

Further information:

• School website
• Graduate School

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• School website
• Staff profiles
• Graduate School
• Open Days
• Order or download a prospectus