Research course

Mathematics

Institution
University of Kent · School of Mathematics, Statistics and Actuarial Science
Qualifications
MSc by researchMPhilPhD

Entry requirements

A first or second class honours degree in a subject with a significant mathematical content (or equivalent).

Months of entry

September

Course content

Studying Mathematics at postgraduate level gives you a chance to begin your own research, develop your own creativity and be part of a long tradition of people investigating analytic, geometric and algebraic ideas. Under the guidance of internationally renowned researchers in the School of Mathematics, Statistics and Actuarial Science (SMSAS), postgraduate students develop analytical, communication and research skills. Developing computational skills and applying them to mathematical problems forms a significant part of the postgraduate training in the School.

The Mathematics Group at Kent ranked highly in the most recent Research Assessment Exercise. With 100% of the Applied Mathematics Group submitted, all research outputs were judged to be of international quality and 12.5% was rated 4*. For the Pure Mathematics Group, a large proportion of the outputs demonstrated international excellence.

The Mathematics Group also has an excellent track record of winning research grants from the Engineering and Physical Sciences Research Council (EPSRC), the Royal Society, the EU, the London Mathematical Society and the Leverhulme Trust.

The research interests of the Mathematics Group cover a wide range of topics following our strategy of cohesion with diversity. The areas outlined provide focal points for these varied interests.



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.

Information for international students

For detailed information see our English language requirements web pages. http://www.kent.ac.uk/ems/eng-lang-reqs/index.html Please note that if you are required to meet an English language condition, we offer a number of pre-sessional courses in English for Academic Purposes through Kent International Pathways. See http://www.kent.ac.uk/international-pathways/

Fees and funding

Please visit our

funding web pages

for the most current information and application details.

Qualification and course duration

MSc by research

full time
12 months
part time
24 months

MPhil

full time
24 months
part time
36 months

PhD

full time
36 months
part time
60 months

Course contact details

Name
School of Mathematics, Statistics and Actuarial Science
Email
smsaspgadmin@kent.ac.uk
Phone
+44 (0)1227 824133