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The University of Kent, Canterbury, Kent, CT2 7NZ, T +44 (0)1227 764000
Mathematics MSc, MPhil, PhD
This is a research programme within the Mathematics subject area.
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 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.
Key facts
- Subject area: Mathematics
- Location: Canterbury
- School: School of Mathematics, Statistics and Actuarial Science
- Duration: MSc one year full-time or two years part-time, MPhil two years full-time or three years part-time, PhD registration three to four years full-time or five to six years part-time.
- Start: Any time but preferably in September
- Fees and funding: More info
- Entry requirements: A first or second class honours degree in a subject with a significant mathematical content (or equivalent). Please also check our general entry requirements (including English language requirements).
Research areas
Nonlinear Differential Equations
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.
Painlevé Equations
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.
Mathematical Biology
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.
Quantum Integrable 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
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.
Algebra and Representation Theory
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
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.
Financial Mathematics
Research includes work on financial risk management, asset pricing and optimal asset allocation, along with models to improve corporate financial management.
Show all
|Key facts
- Subject area: Mathematics
- Location: Canterbury
- School: School of Mathematics, Statistics and Actuarial Science
- Duration: MSc one year full-time or two years part-time, MPhil two years full-time or three years part-time, PhD registration three to four years full-time or five to six years part-time.
- Start: Any time but preferably in September
- Fees and funding: More info
- Entry requirements: A first or second class honours degree in a subject with a significant mathematical content (or equivalent). Please also check our general entry requirements (including English language requirements).
Staff research
Full details of staff research interests can be found on our website.
Dr Antonis Alexandridis: Lecturer in Finance
Artificial intelligence and financial engineering including financial derivative modelling, pricing and forecasting, weather risk management, machine learning, computer science, neural and wavelet networks, stochastic calculus, wavelet analysis and signal denoising.
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 in 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: Senior Lecturer in Mathematics
Analysis, metric geometry and combinatorics; applications in optimal control, game theory and computer science. Recent publications include: Nonlinear Perron-Frobenius Theory (co-author, 2012).
Professor Elizabeth L Mansfield: Professor of Mathematics
Nonlinear differential and difference equations; variational methods; moving frames and geometric integration. Recent publications include: A Practical Guide to the Invariant Calculus (2010).
Dr Jaideep Oberoi: Lecturer in Finance
Identification and quantification of liquidity risk in financial markets and the implications of incomplete information for asset price co-variation.
Dr Rowena Paget: Lecturer in Pure Mathematics
Representation theory of groups and algebras, with emphasis on algebras possessing a quasi-hereditary 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. Recent publications include: Gröbner Bases in Symbolic Analysis (co-ed, 2007).
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 Huamao Wang: Lecturer in Finance
Developing mathematical models; numerical methods and practical application of portfolio optimisation; derivative pricing and hedging; risk management based on stochastic calculus, optimal control, filtering and simulation.
Dr Jing Ping Wang: Senior 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:
Key facts
- Subject area: Mathematics
- Location: Canterbury
- School: School of Mathematics, Statistics and Actuarial Science
- Duration: MSc one year full-time or two years part-time, MPhil two years full-time or three years part-time, PhD registration three to four years full-time or five to six years part-time.
- Start: Any time but preferably in September
- Fees and funding: More info
- Entry requirements: A first or second class honours degree in a subject with a significant mathematical content (or equivalent). Please also check our general entry requirements (including English language requirements).
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
Key facts
- Subject area: Mathematics
- Location: Canterbury
- School: School of Mathematics, Statistics and Actuarial Science
- Duration: MSc one year full-time or two years part-time, MPhil two years full-time or three years part-time, PhD registration three to four years full-time or five to six years part-time.
- Start: Any time but preferably in September
- Fees and funding: More info
- Entry requirements: A first or second class honours degree in a subject with a significant mathematical content (or equivalent). Please also check our general entry requirements (including English language requirements).
How to apply
Before applying, please read our ‘How to apply’ section.
You can then go straight to the online application form by clicking the programme below:
Key facts
- Subject area: Mathematics
- Location: Canterbury
- School: School of Mathematics, Statistics and Actuarial Science
- Duration: MSc one year full-time or two years part-time, MPhil two years full-time or three years part-time, PhD registration three to four years full-time or five to six years part-time.
- Start: Any time but preferably in September
- Fees and funding: More info
- Entry requirements: A first or second class honours degree in a subject with a significant mathematical content (or equivalent). Please also check our general entry requirements (including English language requirements).