Admissions enquiries T: +44 (0)1227 827272 E: information@kent.ac.uk
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.
Staff research interests Full details of staff research interests can be found on our website: www.kent.ac.uk/smsas/staff 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.
www.kent.ac.uk/smsas
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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.
Professor Peter Fleischmann: Professor of Pure Mathematics Representation theory and structure theory of finite groups; constructive invariant theory; applied algebra and discrete mathematics.
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.
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 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 Steffen Krusch: Lecturer in Applied Mathematics Topological solitons in mathematical physics, in particular the classical and quantum behaviour of skyrmions.
Dr Chris Woodcock: Senior Lecturer in Pure Mathematics P-adic analogues of classical functions; commutative algebra; algebraic geometry; modular invariant theory.
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 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. Recent publications include: Gröbner Bases in Symbolic Analysis (co-ed, 2007).
Location Canterbury.
English language requirements See p211.
Fees and funding See www.kent.ac.uk/pgfunding
National ratings Most recent Research Assessment Exercise: 45% of our applied mathematics research and 35% of our pure mathematics research was rated “world-leading” or “internationally excellent”, with a further 55% of each judged as “internationally recognised”. Kent was ranked 1st in the UK for mathematics graduate employment prospects in The Complete University Guide 2012.
Applications Taught programmes Online at www.kent.ac.uk/courses/ postgrad/apply Research programmes See p218 or contact the School for further details.
Further information T: +44 (0)1227 824133 E: smsaspgadmin@kent.ac.uk