Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
Samson Abramsky is Professor of Computer Science at University College London. He was previously the Christopher Strachey Professor of Computing at Wolfson College, Oxford, from 2000 to 2021.
Dame Mary Lucy Cartwright was a British mathematician. She was one of the pioneers of what would later become known as chaos theory. Along with J. E. Littlewood, Cartwright saw many solutions to a problem which would later be seen as an example of the butterfly effect.
Richard Peter Stanley is an Emeritus Professor of Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. From 2000 to 2010, he was the Norman Levinson Professor of Applied Mathematics. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota. He is an expert in the field of combinatorics and its applications to other mathematical disciplines.
Sir David Roxbee Cox was a British statistician and educator. His wide-ranging contributions to the field of statistics included introducing logistic regression, the proportional hazards model and the Cox process, a point process named after him.
The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. In algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial designs and the theory of error-correcting codes. In algebra, association schemes generalize groups, and the theory of association schemes generalizes the character theory of linear representations of groups.
Dusa McDuff FRS CorrFRSE is an English mathematician who works on symplectic geometry. She was the first recipient of the Ruth Lyttle Satter Prize in Mathematics, was a Noether Lecturer, and is a Fellow of the Royal Society. She is currently the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College.
Peter Jephson Cameron FRSE is an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory. He is currently half-time Professor of Mathematics at the University of St Andrews, and Emeritus Professor at Queen Mary University of London.
Cheryl Elisabeth Praeger is an Australian mathematician. Praeger received BSc (1969) and MSc degrees from the University of Queensland (1974), and a doctorate from the University of Oxford in 1973 under direction of Peter M. Neumann. She has published widely and has advised 27 PhD students. She is currently Emeritus Professor of Mathematics at the University of Western Australia. She is best known for her works in group theory, algebraic graph theory and combinatorial designs.
John Halstead Hardman Moore CBE FBA FRSE is an economic theorist. He was appointed George Watson's and Daniel Stewart's Chair of Political Economy at the University of Edinburgh School of Economics in 2000. In 2018 he was appointed the David Hume University Professor at the University of Edinburgh. Previously, in 1983, he was appointed to the London School of Economics, where in 1990 he became Professor of Economic Theory, a position he still holds.
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
Algebraic statistics is the use of algebra to advance statistics. Algebra has been useful for experimental design, parameter estimation, and hypothesis testing.
Edmund Frederick Robertson is a professor emeritus of pure mathematics at the University of St Andrews.
In mathematics, a Bose–Mesner algebra is a special set of matrices which arise from a combinatorial structure known as an association scheme, together with the usual set of rules for combining those matrices, such that they form an associative algebra, or, more precisely, a unitary commutative algebra. Among these rules are:
Norman Linstead Biggs is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics.
Walter Ledermann FRSE was a German and British mathematician who worked on matrix theory, group theory, homological algebra, number theory, statistics, and stochastic processes. He was elected to the Royal Society of Edinburgh in 1944.
Kenneth John Falconer is a British mathematician working in mathematical analysis and in particular on fractal geometry. He is Regius Professor of Mathematics in the School of Mathematics and Statistics at the University of St Andrews.
Fang Kaitai, also known as Kai-Tai Fang, is a Chinese mathematician and statistician who has helped to develop generalized multivariate analysis, which extends classical multivariate analysis beyond the multivariate normal distribution to more general elliptical distributions. He has also contributed to the design of experiments.
James William Peter Hirschfeld is an Australian mathematician, resident in the United Kingdom, specializing in combinatorial geometry and the geometry of finite fields. He is an emeritus professor and Tutorial Fellow at the University of Sussex.
Martin Liebeck is a professor of Pure Mathematics at Imperial College London whose research interests include group theory and algebraic combinatorics.
