David Arrowsmith is co-leader of a group of mathematicians and electronic engineers who use chaotic dynamical systems to model telecommunications networks. He simulates the phenomenon of long-range dependence of internet traffic and develops control techniques for congestion reduction in computer networks.
R. A. Bailey's interests are in design of experiments. This research is motivated by problems arising in experiments in a number of scientific areas, such as: if we are experimenting on sprays to deter aphids, does it matter what spray is on the neighbouring plot? In turn, this spills over into pure combinatorics, such as Latin squares and association schemes.
Christian Beck works on nonlinear dynamical systems and their applications. In particular, he is interested in the interplay between dynamical systems, statistical mechanics and stochastic processes. He is also working on spatio-temporal chaos as generated by coupled map lattices. Applications include fully developed hydrodynamic turbulence and stochastically quantized field theories.
Barbara Bogacka researches experimental designs for linear and non-linear models of observations. She is particularly interested in what makes the best design for parameter estimation, hypotheses testing, and discriminating between different models. These designs are applied in agriculture, biology and chemistry.
Shaun Bullett studies the dynamics of complex maps, Kleinian groups and holomorphic correspondences. This is an area of mathematics in which there is a rich interplay between complex analysis, hyperbolic geometry, topology and symbolic dynamics. It has grown rapidly in the last twenty years with the advent of microcomputers, bringing stunning illustrations of fractal limit sets, but the pure mathematics involved has its origins in the great mathematical advances of earlier centuries.
Peter Cameron's interests include permutation groups, and the (finite or infinite) structures on which they can act (which may be designs, graphs, codes, geometries, etc.). Those countably infinite structures with the most symmetry are the ones which can be specified by first-order logical axioms; this is a general framework which includes many counting problems for types of finite structures.
Ian Chiswell works in combinatorial group theory, where his main interest is in generalised trees and actions of groups on them. This is an area having important connections with logic and low-dimensional topology. The theory of R-trees in particular has expanded enormously in the last 15 years. Other interests include equations over groups, right-ordered groups and, less recently, cohomology of groups.
Cho-Ho Chu's research is in Analysis, but it is also related to group representations, non-associative algebras, differential geometry and probability theory. The main areas of my current research are harmonic analysis and integral equations on groups; Jordan algebras and analysis on infinite-dimensional manifolds; and operator algebras and functional analysis.
Matthew Fayers is an algebraist who works mostly with representations of finite-dimensional algebras, especially group algebras of symmetric groups (and other Coxeter groups) and the related Hecke algebras and Schur algebras. He is particularly interested in calculating decomposition matrices and module structures, and specialises in exploiting combinatorics (of partitions, Young diagrams and the abacus) rather than technical algebraic machinery.
Steven Gilmour's interests are in statistical aspects of the design and analysis of experiments, particularly experiments with complex treatment structures. This includes treatments which are combinations of several factors, treatments which are levels of a continuous factor and treatments which are combinations of levels of several continuous factors (response surface experimentation). This research is driven by problems arising in applications, particularly in the food, pharmaceuticals, chemicals and bioprocessing industries and the related sciences such as food science, biotechnology and biochemistry.
Ilya Goldsheid is working on mathematical problems concerned with models arising in the theory of solid state matter, including the celebrated Anderson model; the classical localization theory and the theory of non-self-adjoint models; and random walks in random environments. The approach to these models is based on the theory of products of random matrices, the spectral analysis of random operators, dynamical systems methods, and probability theory.
Anthony Hilton's interests lie in Graph Theory and Design Theory. In graph theory he works on edge and total colourings and on decompositions of graphs. In design theory he works on embedding partial designs into complete designs, particularly simple designs such as latin squares and Steiner triple systems. He explores the grey area where graph and design theory interact, and introduced the new area of amalgamation and disentanglement of designs. He has also worked on extremal set theory and on continuous maps between graphs as 1-dimensional complexes.
Wilfrid Hodges works in model theory (logic), where his main interests are automorphism groups, definability and the cohomological links between these two. He also works on mathematical semantics of natural and formal languages, and in particular on situations where the grammar and the meaning of phrases don't match up.
Bill Jackson's interests are in combinatorics, particularly graph theory, matroid theory and combinatorial algorithms. He is currently working on problems concerning graph connectivity, rigidity of frameworks, graph polynomials, and orientations of graphs.
Mark Jerrum is interested combinatorics, computational complexity and stochastic processes. All of these ingredients come together in the study of randomised algorithms: computational procedures that exploit the surprising power of making random choices. A strong theme in this work is the analysis of the mixing time of combinatorially or geometrically defined Markov chains.
Robert Johnson's research is in combinatorics and graph theory. He is particularly interested in extremal combinatorics, and problems at the interface of graphs and set systems.
Oliver Jenkinson works on the ergodic theory of chaotic dynamical systems, and its applications to other branches of mathematics such as number theory, geometry, and complex function theory. Current areas of interest include thermodynamic formalism, ergodic optimization, continued fractions, and algorithms for computing geometric and dynamical invariants.
Wolfram Just applies equilibrium statistics to dynamical systems, studying pattern formation and phase transitions in spatially extended dynamical models. Other interests include the control of chaotic behaviour by time-delayed feedback.
Boris Khoruzhenko is interested in random matrices and operators. He currently works on statistical properties of eigenvalues of non-Hermitian random matrices. Such matrices have recently attracted much interest in mathematics and mathematical physics due to their surprising properties.
Rainer Klages studies applications of dynamical systems theory to nonequilibrium statistical mechanics. A major research theme are the chaotic and fractal properties of transport in low-dimensional models, where unexpected phenomena like fractal transport coefficients are encountered. More recently he became interested in anomalous transport, bouncing balls and the modeling of biological cell migration.
Charles Leedham-Green is the driving force behind the "matrix group recognition project", which aims to determine a group from a set of matrices generating it. It has been known that this computational problem is much more difficult than the analogous question for permutation groups. His other interests lie in the field of p-groups and pro-p-groups.
Angus Macintyre's
main research interest is mathematical logic which has involved research in
group theory, algebraic geometry, number theory and neural methods.
Malcolm MacCallum is interested in most aspects of classical non-Newtonian
gravity, especially general relativity, applying geometric and algebraic methods
to physical problems. Particular interests include cosmological models, black
holes, gravitational waves, asymptotics of spacetimes and exact solutions of
the field equations. He also works on applications of computer algebra, in ordinary
differential equations as well as in gravity theory.
Shahn Majid is interested in algebraic structures on the interface between pure mathematics and mathematical physics including quantum gravity. Particularly: noncommutative differential geometry; quantum groups or Hopf algebras with applications in representation theory and knot theory; and noncommutative geometry of discrete systems as a (noncommutative) Lie theory for finite groups.
Susan McKay is a group theorist primarily interested in p-groups. She has worked on p-groups of finite coclass, and its generalizations, that have seen spectacular successes in recent years. She is responsible for extensive investigations of such remarkable groups as the Grigorchuk and Nottingham groups.
Thomas Müller studies the function giving the number of subgroups of given index in a finitely generated group. He is concerned both with the growth rate of this function, and with divisibility and arithmetic properties. This work involves algebra, combinatorics, and analysis, and has implications for subjects such as Quillen complexes.
Lawrence Pettit is a Bayesian statistician. His main work has concentrated on outliers and model choice in a variety of areas including linear models, finite populations and time series. He is also currently interested in classification and regression trees, degradation models and inference for Lanchester models.
Donald Preece's research is into classes of combinatorial designs that include non-orthogonal Graeco-Latin designs, neighbour designs and tight single-change covering designs. These designs have had applications in the methodology of statistics, many of them as designs for comparative experiments in quantitative biological research. The research involves use of group theory and number theory.
Thomas Prellberg is a mathematical physicist working in the areas of statistical mechanics and dynamical systems. His studies of lattice models of polymers employ methods of enumerative combinatorics as well as a class of Monte Carlo algorithms which perform "approximate counting." Applications range from simple self-avoiding random walks to detailed models of e.g. the response of proteins to micromechanical deformation. Other interests include non-uniformly expanding dynamical systems, employing spectral analysis of transfer operators.
Linda Rass is interested in mathematical modelling in biology, covering such aspects as epidemics, genetics, evolutionary games, and branching processes. She uses both deterministic and stochastic techniques to investigate spatial and non-spatial models.
Leonard Soicher uses computation to investigate groups and combinatorial structures. He is closely involved with GAP, the computer system for group theory and discrete mathematics, and has developed a share package for studying graphs, in which the symmetries of a graph are exploited to search more efficiently. This package is widely used in the group theory and combinatorics communities. Some of the designs he has found are motivated by statistical applications.
Dudley Stark works in probabilistic combinatorics, the study of randomly chosen combinatorial structures. The motivation for his field is twofold. Firstly, combinatorial objects with average properties may be difficult to construct explicitly and so proving their existence may require probabilistic methods. Secondly, randomly chosen combinatorial structures can be good models for physical or computational systems.
Roger Sugden's interests are in statistical inference based on complex samples from a finite population. He has worked on sufficiency, exchangeability, ignorability, Edgeworth expansions for sample size determination, and is currently working on exact design-based linear estimation. The work is applicable to the analysis of complex sample survey data.
Ivan Tomasic studies model theory (a branch of logic) and applications in algebraic geometry and number theory. More specifically, his interests include arithmetic aspects of the Frobenius automorphism, geometry of fields with measure, (nonstandard) cohomology theories and motivic integration.
Franco Vivaldi's research lies at the interface between dynamical systems and algebra, with emphasis on arithmetical phenomena underlying strongly chaotic motions. Applications include the study of round-off errors in computer representations of dynamical systems.
Bert Wehrfritz researches in algebra, especially group theory and related areas of ring and module theory. His current interest is finitary groups of various types; the theory of finitary groups has enjoyed a massive expansion over the last decade or so with much work in both Europe and North America.
Robert Wilson works in finite group theory, and related areas such as representation theory, some aspects of combinatorics, and computational techniques and algorithms applicable to finite groups. He is the architect of the web-based "Atlas of Group Representations" and is especially interested in the sporadic simple groups, including the (in)famous Monster group.
Francis Wright works in mathematical computation, especially algebraic and symbolic computation. His current interests include symbolic/numeric solution of problems in the optimum design of experiments, exact symbolic solution of differential equations, and interactive mathematics via the web.