Mathematics and Statistics (PhD / MPhil) - 2012/2013 entry

• Our PhD/MPhils aim to train you to conduct research of a high academic standard and to make original contributions to the subject. The programme involves coursework (where suitable) and research training, but its major component is the preparation of a substantial research thesis. The thesis should demonstrate a sound understanding of the main issues in the area and add to existing knowledge.
• Research interests in mathematics and statistics include: mathematical finance, in particular the analysis of risk and numerical computation; mathematical physics and partial differential equations; approximation theory and numerical analysis; probability and stochastic processes, pure and applied; applied statistics and multivariate analysis; covariance modelling for repeated measures and longitudinal data; medical statistics; combinatorics, algebra and designs.

• As a research student, you will have access to a wide range of study resources, including the University of London seminar programme in probability and statistics, excellent library facilities close by in Bloomsbury and the taught courses and project component of our MSc Applied Statistics programmes. Extensive computing facilities include PCs and UNIX platforms.

• Generic courses and workshops are offered by the College.

Admission and registration

Applications are considered throughout the year. A brief research proposal should be submitted with the application form. For suitably qualified candidates, the Admissions Tutor will circulate this to potential supervisors. If the proposed topic falls within the department's area of interest, the candidate's referees will be contacted and he or she may be invited for interview. The final decision on admittance is taken by a department group consisting of, as a minimum, the Chairman, the Postgraduate Admissions Tutor and the prospective supervisor.

Students must register for an MPhil in the first instance but may subsequently transfer to PhD without loss of time if progress is satisfactory. The MPhil degree is a research degree examined by thesis and it must be either a record of original work or an ordered and critical exposition of existing knowledge. The thesis submitted for the PhD degree must form a distinct contribution to the knowledge of the subject; it must afford evidence of originality, shown either by the discovery of new facts or by the exercise of independent critical power.

Overseas students (who have not been resident in the UK for at least three years immediately prior to the start of their course) are not eligible for part-time registration, and should have secured sufficient funding before pursuing an application.

Office space

Some permanent office accommodation is available for full-time research students, and teaching rooms are normally available during the day for part-time students to work in.

• To ensure that we have an appropriate supervisor for your area of research, you should contact the course team to discuss it before submitting your application.

• Andris Abakuks, BA, MA, DPhil, CStat: Application of probability and statistics to problems in theology and New Testament studies; applied statistics, for example problems arising from geographical survey data; applied stochastic processes and Markov decision processes, especially models for epidemics and biological population growth.
• Brad Baxter, BA, PhD: Approximation theory; numerical analysis; mathematical finance; theory and algorithms of radial basis functions.
• Andrew Bowler, BSc, MSc, PhD: Symmetric designs; Latin squares; quasigroups and non-associative algebra.
• Anthony Brooms, BSc, MSc, PhD: Stochastic processes; stochastic order results; stochastic games, with applications to models of service systems; optimisation and control.
• Professor Raymond Brummelhuis, Doctoraal examen, PhD: Mathematical finance; mathematical physics and particle differential equations.
• Professor Hélyette Geman, PhD (Maths), PhD (Finance), Agrég. Maths, Agrég. Gestion: Interest rates and inflation derivatives; levy processes in financial modelling; oil, natural gas, carbon and electricity spot prices; stochastic modelling of commodity forward curves; real options in the oil and gas industry; securitisation of catastrophic risk; hedge funds; dependence structure and derivatives.
• Sarah Hart, BSc, MSc, PhD: Group Theory – sum-free sets, Coxeter groups, commuting graphs.
• Simon Hubbert, BSc, PhD: Numerical analysis; approximation theory;  mathematical risk management.
• Maura Paterson, BSc, PhD: Information security; combinatorics.
• Amarpreet Rattan, BSc, MMath, PhD: Enumerative and algebraic combinatorics: combinatorics and representation theory of symmetric group and lattice path combinatorics. 
• Simon Skene, BSc, MSc, PhD: Medical statistics; covariance modelling for repeated measures and longitudinal data; small samples; multivariate analysis techniques.
• Jing Xu, BSc, MSc, PhD: Biostatistics; repeated measures and longitudinal data; covariance modelling; constrained statistical inference. 

• Non-associative algebras and normal ideals
• Canonical auto and cross correlations of multivariate time series
• Dimension and measure defined by infinite Bernoulli convolutions
• Some Markov decision models for pest control
• Aspects of estimation in linear and non-linear time series models
• Inventory renewal time series and their ARMA equivalents
• Some statistical aspects of the estimation of fire losses
• The use of tensor algebras in population genetics.

• You can apply, and start studying, at any time during the year.