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.
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.
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.
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.
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.
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. He is responsible for the website DesignTheory.org.
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.
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 Finite Group Representations, and is especially interested in the sporadic simple groups, including the (in)famous Monster group.
Page
maintained by Peter J. Cameron
1 September 2006