Maxwell Institute
We are part of the Maxwell Institute for Mathematical Sciences partnership with Edinburgh University, and we share our research activities. There are currently 90 academic members of staff and 20 or so postdoctoral research fellows and research assistants in the Maxwell Institute. The departments involved are highly rated: in the 2001 RAE exercise, HeriotWatt University achieved grade 5s for both Applied Mathematics and for Statistics & OR, whilst the University of Edinburgh achieved 5* in Pure Mathematics, 5 in Applied Mathematics, and 4 in Statistics & OR.
The Maxwell Institute covers a very wide spectrum of research in mathematics and in its applications, and we describe below our main strands of interest in the HeriotWatt Mathematics department.
Areas of Research  HeriotWatt Mathematics
Algebra and number theory 

The main areas of research of the Algebra and Number Theory group are: representation theory, algebraic combinatorics, noncommutative algebra, quantum algebras, Lie algebras and automorphic forms, commutative algebra, algebraic geometry, algebraic number theory, algorithmic aspects of algebraic curves, combinatorial aspects of network design, geometric group theory, homological algebra, combinatorial and geometric semigroup theory, automata and languages. The group has close links with the Geometry and Mathematical Physics research groups within the Maxwell Institute. There have also been recent interactions with the Analysis and Statistics groups. HeriotWatt researchers: J Howie, ND Gilbert, MV Lawson, AR Prince 
Analysis 

The Analysis group works on a wide range of topics. Our particular strengths lie in harmonic analysis, spectral theory, linear and nonlinear elliptic, hyperbolic and parabolic PDEs, dynamical systems, stochastic analysis including stochastic nonlinear PDEs, foundations of numerical analysis and applications of the above to problems of physics, continuum mechanics, etc... The group has active links with most of the other groups in the Maxwell Institute including Applied Mathematics, Geometry and Topology, Computational Analysis and Probability. We run a very active joint research seminar and a working group seminar.
HeriotWatt researchers:
L Boulton,

Applied mathematics 

Research activities in Applied Mathematics cover a wide range of topics, many related to differential equations  ordinary, partial and stochastic  and dynamical systems. They include nonlinear waves, such as solitons, with applications to optoelectronics and continuum mechanics, electromagnetic and elastic wave propagation in complex and composite media, stellar dynamics and Hamiltonian mechanics, and fluid, solid and statistical mechanics. There are applications to oilreservoir modelling, geophysical and astrophysical systems, turbulence, combustion, phase transitions and freeboundary problems, and to more general industrial and social modelling. The mathematical methods employed range from asymptotic techniques, in particular exponential asymptotics and homogenisation, to dynamicalsystem techniques, analysis and numerical methods.
There are close links between Applied Mathematics and other activities within the Maxwell Institute, such as Computational Mathematics, Mathematical Biology, Mathematical Physics, Pure and Applied Analysis, and Probability and Stochastics. Regular seminars are organised for postgraduate students and staff. HeriotWatt researchers: E Buckwar, J Carr, DB Duncan, JC Eilbeck, AA Lacey, GJ Lord, SJA Malham, RJ Knops 
Computational mathematics 

Research in computational mathematics covers a broad range of different areas and has strong interdisciplinary links. The focus of our work is on integrated modelling, formulation, analysis and numerical algorithms for differential equations, including ODEs, PDEs, integrodifferential equations and stochastic DEs. Of particular interest is the development of innovative discretisation methods and on the approximation of spectral properties of differential operators. Research topics are varied; some examples include the use of computer algebra to analyse integrable systems, the development and analysis of geometric integrators, the design of efficient numerical schemes for multiple scale modelling, stochastic PDEs and quantum lattice dynamics. Applications arise from diverse areas of science and engineering, including biomedical science, finance, fluid dynamics, material science, molecular dynamics, modelling of neurons, oil reservoir simulation, phase transitions and wave propagation. There are close connections between Computational Mathematics and other activities within the Maxwell Institute, such as Applied Mathematics, Mathematical Biology, Mathematical Physics, Pure and Applied Analysis, and Probability and Stochastics. Collaborations are in place with other major research groups in computational mathematics based throughout the UK and the world. HeriotWatt researchers: L Banas, L Boulton, E Buckwar, JC Eilbeck, DB Duncan, GJ Lord, SJA Malham 
Geometry and topology 

The main areas of research of the geometry and topology group are algebraic geometry, algebraic topology, differential geometry, geometric group theory and surgery theory. More specific research areas include birational geometry (especially of 3folds), Kaehler geometry, topics in gauge theory, geometry of moduli spaces and highdimensional manifolds and knottheory. The group has links with the following research groups within the Maxwell Institute: Algebra, Analysis, and Mathematical Physics. HeriotWatt researchers:
J Howie,

Mathematical biology 

Research in mathematical biology concerns the application of mathematics to cell biology, medicine, ecology and evolution. Some of our work is focussed on specific applications and is done in collaboration with experimental biologists or field ecologists. Other work is more theoretical in nature, developing fundamental modelling techniques with potential applications to a wide range of biological problems. Our models include ordinary and partial differential equations, and spatially discrete models such as cellular automata. HeriotWatt researchers: KJ Painter, JA Sherratt, AR White 
Mathematical physics 

The Edinburgh Mathematical Physics Group consists of 15 permanent academic staff, 6 postdoctoral research fellows and 13 postgraduate students. Our main areas of research are string and Mtheories, classical and quantum integrable systems, topological quantum field theories, lowdimensional quantum gravity, statistical mechanics of random surfaces; although our interests are varied and span a wide range of topics in modern mathematics and physics. We have close ties with the Algebra and Topology/Geometry groups. Our regular research activities include a weekly seminar series, as well as student seminars and journal clubs on a variety of topics, most recently generalised geometry and Dbranes. We have our own preprint series which contains most of our research output. HeriotWatt researchers: JC Eilbeck, DA Johnston, A Konechny, O Penrose, BJ Schroers, RJ Szabo, RA Weston 