# Research Interests of Staff

### A-Z Index: A - C D - F G - J K - N O - R S - V W - Z -- Emeriti

- David Abrahams Diffraction and propagation of acoustic, elastic, electromagnetic and water waves; mathematical methods including asymptotic techniques, homogenisation methods, complex variable theory and systems of equations of Wiener-Hopf type; other areas include fracture mechanics, geophysical flows and mathematical finance.
- Peter Aczel Mathematical Logic: Philosophy and foundations of mathematics. Constructive Mathematics, particularly constructive point-set and point-free topology. Constructive set theory. Dependent type theory. Dependently sorted logic.
- Christopher Baker Analysis, Numerical Analysis, Modelling (particularly in bio-mathematics), Volterra integral and integro-differential equations, Deterministic and Stochastic retarded and neutral differential equations.
- Yuri Bazlov Hopf algebras and quantum groups, applications to representation theory, combinatorics and integrable systems.
- Alexandre Borovik Group theory in its various aspects, combinatorics, model theory. Non-deterministic and probabilistic methods in discrete mathematics.
- Georgi Boshnakov Time series analysis, probability distributions, prediction, symbolic computation, stochastic processes.
- Dave Broomhead Nonlinear dynamical systems, iterated function systems, dynamical systems approach to time series analysis and signal processing, dynamics in mathematical biology, e.g. models of neural systems, fractal models of neurons.
- Roger Bryant Free Lie algebras, finitely presented Lie algebras, representations of groups, varieties of groups.
- Mark Coleman Analytic Number Theory with special interest in the "geometric" distribution of ideals in number fields and the distribution of Gaussian primes in the plane. Hecke L-functions with Groessencharaktere. Sieve methods.

### D - F

- Joel Daou Combustion, fluid mechanics, numerical and asymptotic methods, heat transfer and mixtures thermodynamics.
- John Dold Combustion theory , Modelling of Physical and Biological Systems.
- Alex DonevExperimental design, biostatistics, medical statistics, industrial statistics, linear and non-linear mixed models, statistical computing, statistical consultancy
- Ron Doney Stochastic processes: particularly random walks, Brownian motion, and Lévy processes (the continuous analogue of random walks).
- Peter Duck Fluid mechanics.
- Charles Eaton Representation theory of finite groups.
- Peter Eccles The application of algebraic topology and homotopy theory to differential topology, in particular the self-intersection manifolds of self-tranverse immersions. Infinite loop spaces. Stable homotopy theory.
- Sergei Fedotov Nonlinear Waves, Dynamo Theory, Random Walks and Turbulence, Mathematical Biology, Combustion Theory, Finance modelling.
- Peter Foster Nonparametric density and regression estimation, Multivariate statistics.

### G - J

- Jitesh Gajjar High Reynolds number fluid flows from a theoretical and computational viewpoint, computational fluid dynamics, parallel programming, hydrodynamic stability theory, asymptotic methods.
- Paul Glendinning Pure and applied dynamical systems, Global bifurcation theory, coupled map lattices, one dimensional maps, strange nonchaotic attractors, quasi-periodically forced systems. Biological applications.
- Nico Gray Continnum mechanics, granular materials, hyperbolic systems, avalanches, shock waves, particle-size segregation, mixing, pattern formation, debris-flows, pyroclastic flows and sea-ice dynamics, using a combination of theory, numerics and experiments.
- Dave Harris Mechanics of granular materials, continuum and discrete mechanics, constitutive equations, hyperbolic partial differential equations, boundary and initial value problems, modelling.
- Andrew Hazel Biological Fluid and Solid Mechanics, Fluid-Structure Interaction, Transport Processes, Scientific Computing, Non-linear Dynamics.
- Matthias Heil Computational (bio-)mechanics. Fluid and solid mechanics, especially large-displacement fluid-structure interaction problems. Scientific computing (finite element methods, adaptivity, physics-based preconditioning).
- Richard Hewitt Theoretical, computational and experimental fluid dynamics.
- Nick Higham Numerical analysis, numerical linear algebra, matrix functions, eigenvalue problems, stability of algorithms.
- Jerry Huke Dynamical systems theory and its applications. Embedding and reconstruction theory and its extension to stochastic and spatiotemporal systems. Nonlinear signal analysis and processing.
- Marianne Johnson Group actions on free Lie algebras, torsion in groups and homology of Lie powers, tropical mathematics.
- Anne Juel Instabilities and bifurcations in fluid flows, through a close interplay between theoretical analysis and careful experimentation. Pattern formation in particle-laden flows. Biomechanics and fluid-structure interaction.

### K - N

- Mark Kambites Combinatorial and geometric group theory, semigroup theory, formal languages and automata, computational complexity, parallel processing, cryptography and interactions between the above.
- Hovik Khudaverdyan Differential geometry. In particular geometry of supermanifolds and its applications. Mathematical Physics: cohomology in physics, mathematical problems in quantum physics.
- Eos Kyprianou Statistics.
- Bill Lionheart Reconstruction algorithms for electrical and electromagnetic imaging. Specifically Medical and Industrial Electrical Impedance and other forms of Tomography. Uniqueness and reconstruction for anisotropic inverse problems in electromagnetics and optics (analysis and differential geometry).
- Mick McCrudden Probabilities on algebraic structures. Embedding theorems for infinitely divisible probabilities on Lie groups, and Lie semigroups. Support and density properties of Gauss semigroups on Lie groups.
- Gábor Megyesi Algebraic geometry, enumerative geometry, geometry in finite characteristic.
- James Montaldi Hamiltonian dynamics and symmetry, symplectic geometry, (local) geometry of momentum maps and its effects on dynamics, bifurcations.
- David Moss Astrophysical magnetohydrodynamics: dynamo theory; the origin and evolution of stellar magnetic fields; the generation and maintenance of galactic magnetic fields, and their influence on the interstellar medium.
- Mark Muldoon Applied nonlinear dynamics, especially involving the life sciences or signal processing: models of molecular evolution and phylogenetics, applications to HIV vaccine development, models of cellular regulation and stochastic resonance in vision.

### O - R

- Jianxin Pan Longitudinal and spatial data analysis, survival analysis, generalized linear mixed models, linear and non-linear mixed models, growth curve models, covariance modelling, nonparameteric smoothing, statistical diagnostics, state-space modelling, Baysian analysis, computational statistics, Biostatistics and medical statistics.
- Jeff Paris Inductive Logic, Uncertain Reasoning and Probability Logic, with especial reference to explicating and investigating principles of rationality or common sense.
- Goran Peskir Brownian motion, stochastic calculus, Markov processes, optimal stopping, optimal stochastic control, financial mathematics.
- Roger Plymen K-Theory & Analysis: K-theory of operator algebras, Plancherel measure. Noncommutative geometry and number theory, especially the local Langlands conjectures.
- Catherine Powell Mixed finite element formulations, numerical linear algebra, preconditioning, fast solvers, algebraic multigrid.
- Alexander Premet Lie Theory, Representation Theory and Geometric Invariant Theory: representation theory of restricted Lie algebras and algebraic groups; quantization of Slodowy slices and primitive ideals; classification of finite dimensional simple Lie algebras over fields of positive characteristic; nilpotent orbits, commuting varieties and centralizers in semisimple Lie algebras.
- Mike Prest Modules, representations of algebras, model theory, geometric representation theory, model theory in categories, non-commutative geometry.
- Nige Ray Algebraic topology: cobordism theory, cohomology operations, complex oriented cohomology theory, K-theory, loop spaces, model category theory, stable homotopy theory, toric topology. Geometry: toric manifolds and related combinatorial constructions, weighted projective spaces.
- Peter Rowley Finite Simple Groups, Amalgams of groups and completions of amalgams, Group Geometries, Point-Line Collinearity Graphs of Sporadic Simple Groups, Coxeter Groups, Commuting Graphs, Cages.

### S - V

- Nikita Sidorov Dynamical systems and number theory: Bernoulli convolutions, expansions in non-integer bases, iterated function systems, fractals.
- David Silvester Scientific Computation; fluid dynamics; finite element theory, error estimation; numerical linear algebra, fast solvers, multigrid.
- Mike Simon Fluid dynamics: wave problems, extending into acoustics and elastodynamics, but principally concerned with water waves.
- Toby Stafford Non-commutative algebra, with particular emphasis on its interaction with other areas of mathematics, notably to algebraic geometry, Lie theory and quantum groups. Recent interest in noncommutative geometry and symplectic reflection algebras.
- Colin Steele Mathematical Applications in Astrophysics: Equilibrium and Stability theory. Mechanical, thermal and magnetic terms. First, second and higher order stability. Applied to Solar Prominences, other coronal structures, gas clouds.
- Ralph Stöhr Lie Algebras: Group actions on free Lie algebras. Group Theory: Homological methods in Group Theory, Combinatorial Group Theory, Equations over groups.
- Tata Subba Rao Non-stationary and non-linear time series analysis, higher order spectral analysis, theory of random fields, time series methods for analysis of environmental variables (detection of climatic changes etc), multivariate nonlinear models.
- Peter Symonds Representation theory and cohomology of groups. Particularly interested in profinite groups and group actions on rings.
- Ron Thatcher Numerical analysis; finite element analysis. Applications in modelling fluid flow and modelling flames. Least squares solutions of first order partial differential equations.
- Ruth Thomas Numerical solution of stiff, oscillatory ODEs. Adaptive mesh methods for parabolic PDEs. Numerical strategies for delay differential algebraic equations. Numerical solution of differential/algebraic boundary value problems.
- Francoise Tisseur Numerical analysis, numerical linear algebra, eigenvalue problems, stability of algorithms, structured matrix problems.
- Marcus Tressl Model theory of ordered structures, mainly real closed fields and o-minimal structures. Model theory of commutative rings, in connection with real algebraic geometry. I am also interested in differential algebra and its links to model theory.
- Mike Tso Applied statistics, operational research, discrete and combinatorial optimization, mathematical programming, integer programming, reliability theory, decision analysis, logistics, location models.
- Ted Voronov Differential geometry and topology; mathematical physics. In particular, geometry of supermanifolds and its applications; quantization; bracket structures and homotopy algebras; integral geometry.

### W - Z

- Charles Walkden Smooth ergodic theory, Symbolic dynamics and thermodynamic formalism. Hyperbolic and partially hyperbolic dynamical systems.
- Louise Walker Geometries and graphs related to finite simple groups.
- Alex Wilkie Model theory, especially that of o-minimal theories; analytic and subanalytic sets (both real and complex).
- George Wilmers Mathematical Logic: Reasoning under Uncertainty, Prior Probability Functions , The Philosophical Foundations and Axiomatics of Voting Systems.
- Jingsong Yuan Higher order spectral analysis and modelling of time series and random fields, asymptotic theory of spectral estimation, frequency domain tests and classification, Markov random field modelling, and statistical problems in signal and image processing including texture classification.
- Tusheng Zhang Stochastic Analysis, Dirichlet Forms and Markov Processes.

### Emeritus and Honorary Staff

- David Bell Control theory.
- Kit Dodson Differential geometry, differential topology, connection theory, information geometry, geometry of stochastic processes.
- Patrick Laycock Statistics.
- Ron Ledgard Coding theory.
- Harold Simmons Mathematical logic: decisions problems, model theory, lattice theory, point-free (and point-sensitive) topology, category theory, ring theory and sheaf representations, recursion theory, -calculus, and proof theory.
- Grant Walker Algebraic topology: the structure of the Steenrod algebra, the action of the Steenrod algebra on polynomials. Combinatorics: symmetric functions, Young diagrams and tableaux. Algebra: Modular representation theory of general linear groups in the defining characteristic.
- Reg Wood Action of the Steenrod algebra on polynomials.