The Department of Mathematics and Statistics at the University of Surrey has two EPSRC studentships that are available to support suitably well-qualified candidates on any two of the five projects listed below. For further information on any of the projects, please contact the project supervisor (see below). For further general information, please contact the Postgraduate Admissions Tutor, Dr Ian Roulstone, Department of Mathematics and Statistics, University of Surrey, Guildford GU2 7XH. Tel:01483 689638; Email: I.Roulstone@surrey.ac.uk UK citizens and residents qualify for fees plus a maintenance grant per year for 3 years. EU students qualify for a fees only award. The studentship is not available to citizens of non-EU countries. Applicants require or should be expecting to obtain a 2:1, First Class Honours degree or a Masters degree in Mathematics, or a related discipline. The closing date for the studentship will be 30th June 2005. For general application details please contact Kelly Green, School Postgraduate Administrator: phdadmin@surrey.ac.uk . Please indicate on the front of your application form that it is for the attention of Dr Roulstone. Completed applications should be sent to Kelly Green, Postgraduate Office, School of Electronics and Physical Sciences, University of Surrey, Guildford, Surrey. GU2 7XH. 1. PhD Studentship in Applied Dynamical Systems at the University of Surrey Applications are invited for a PhD studentship in Applied Dynamical Systems, available from October 2005 within the Department of Mathematics & Statistics at the University of Surrey. The aim of this project is to investigate the interaction of patterns on large domains via analytical and numerical techniques. Examples of patterns whose interaction behaviours are of interest are coherent structures with an asymptotic spatially periodic structure and their planar analogues, spiral waves. Such patterns arise in a variety of experiments ranging from chemical reactions to surface waves in fluids to cardiac tissue. How these patterns interact with each other is an exciting and largely unexplored area of research. The thesis project will allow a student to acquire and use modern dynamical systems methods, analytical techniques to study ordinary and partial differential equations, methods from the spectral theory of non-selfadjoint operators, and numerical simulation. For further information please contact Prof Bjorn Sandstede (Tel: 01483 682641; Email: B.Sandstede@surrey.ac.uk). 2. PhD Studentship in Mathematical Biology at the University of Surrey Applications are invited for a PhD studentship in mathematical neurophysiology, available from October 2005 within the Department of Mathematics & Statistics at the University of Surrey. The project will involve developing and analysing models of sensory cells and neural circuits associated with the processing of chemical (e.g. smell, taste) or light stimuli. It is part of an interdisciplinary research theme that aims to understand how sensory inputs are shaped into electrical signals, how successive stages of a neural pathway integrate and modulate activity patterns, and how the system adjusts its responses based on past experience of stimulation. The particular focus of study can be tailored to the student's interests. This research will enable a student to gain skills in mathematical modelling, differential and integral equations, applied dynamical systems methods, optimisation, and numerical simulation. It will also provide opportunities for interaction and collaboration with experimental bioscientists. For further information please contact Dr Alice Yew, Tel: 01483 682636; Email: A.Yew@surrey.ac.uk 3. PhD studentship in Mathematical Models of the Spread of Tuberculosis at the University of Surrey Mathematical models of disease have an important role to play in determining government strategies on how to deal with epidemics, predicting healthcare needs and examining the effectiveness of vaccination programmes. The aim of this project is to extend existing mathematical models of tuberculosis, with the eventual aim of exploring how the disease spreads through a society such as ours that consists of a complex network of social contacts. The project student should have an interest in applying mathematical ideas to biological and sociological systems and should be willing to learn and use a mixture of analytical and computational techniques. For further information please contact Dr Anne Skeldon, Tel: 01483 682634; Email: A.Skeldon@surrey.ac.uk 4. PhD studentship in Numerical Computation of Symmetry Breaking Bifurcations of Periodic Orbits The bifurcation theory of periodic orbits with spatio-temporal symmetries is well-developed, but there are hardly any results on the numerical computation of symmetry-breaking bifurcations. In the package SYMPERCON (developed by Wulff, Schebesch, Hohmann and Deuflhard) only bifurcations which preserve the isotropy are computed. In the package SYMCON by Gatermann and Hohmann symmetry-breaking bifurcations of equilibria are computed by mixed symbolic and numerical methods. The topic of this thesis is to develop numerical techniques for the computation of all generic local symmetry-breaking bifurcations of periodic orbits with standard symmetry groups using the bifurcation theory of Lamb, Melbourne and Wulff and combining the methods from the packages SYMCON and SYMPERCON. The results will be applied to various pattern forming systems, in particular coupled map lattices. For further information please contact Dr Claudia Wulff, Tel: 01483 682630; Email: C.Wulff@surrey.ac.uk 5. PhD studentship in Theory and Numerics of Reversing Symmetry Breaking Bifurcations of Hamiltonian Periodic Orbits Both the theory and numerics of periodic orbits of general dynamical systems is well-developed. But additional structure such as time-reversing and preserving symmetries and symplecticity changes the generic behaviour of dynamical systems dramatically. Recently there has been a lot of progress in the development of a bifurcation theory for symmetric and Hamiltonian systems, but the theory is far from being complete. In particular the bifurcation theory of reversible periodic orbits, although pushed forward a lot by Lamb et al in recent years, is still in its beginning, and there are no methods yet for the numerical detection and computation of bifurcations which break a time-reversal symmetry of a periodic orbit. The topic of this thesis is to analyze such reversing symmetry breaking periodic orbits theoretically and to derive and implement numerical methods for their detection and computation within the package SYMPERCON of Wulff, Schebesch, Hohmann, Deuflhard. The results will be applied to various symmetric Hamiltonian systems, in particular to N-body systems. For further information please contact Dr Claudia Wulff, Tel: 01483 682630; Email: C.Wulff@surrey.ac.uk