Gwyneth Stallard's work has made fundamental contributions to the theory of the dynamics of transcendental complex functions. She has made important discoveries concerning the dimension of Julia sets, and her insight and originality have established major results in the subject. Her work is characterised by the successful application of hard analytic techniques and, as she readily admits, by stubborness.
Faces Of Mathematics
We take a look at some of the people who’ve made major contributions in the world of mathematics.
Marcus du Sautoy has established remarkable results on the structure of finite and infinite groups. Groups are mathematical models of symmetry, exhibiting a great variety of structure and behaviour. In his novel approach to understanding some of this variety, Du Sautoy has used techniques from number theory and analysis that are related to classical methods used to study prime numbers. He is also interested in promoting the wider understanding of mathematics research, and has written a number of articles for The Times and other publications.
Andrew Stuart is a leading numerical analyst, and his work has been at the forefront of the development of computational analysis of evolving systems. He has investigated the relationships between dynamical systems and their computational models, and has contributed theoretical and practical advances in that area, as well as to the study of differential equations. His work is internationally renowned, and has been recognised by the award of numerous prizes.
David Rand's main research work is in mathematical biology. He uses mathematical modelling to study evolutionary and ecological systems, to improve our understanding of the processes of biological change, and to develop new theories about the behaviour of ecological systems. Much of his work is driven by questions arising in experimental biology and in medicine, to which he applies deep mathematical theories and his own creative insights.
Ed Corrigan is Professor of Mathematics at York University. His research is in mathematical physics, in the areas of classical and quantum field theories, and string theory. Corrigan's research aims at solving problems in physics by deepening our understanding of the underlying mathematics. His work involves both ideas inspired by physical systems and ideas arising in diverse areas of pure and applied mathematics.
Frances Kirwan, Professor of Mathematics at the University of Oxford, researches in algebraic and symplectic geometry. Her work endeavours to understand the structure of geometric objects by subtle investigation of their algebraic and topological properties. This work calls on facts and techniques from many other areas of mathematics, as well as requiring a specific ingenuity of its own.
Frank Kelly's research is in applied probability, and his main interest is in the design and control of communication networks. Large-scale networks, such as the Internet, present mathematical and engineering challenges in which randomness is a key feature. Kelly's research embraces both theoretical work in probability, and considerations of its impact and application to the stability and control of modern communication networks.
Gareth Roberts works in applied probability. His research focusses on stochastic processes and their application in computational statistics. He has established crucial results on the Markov chain Monte Carlo technique, an essential part of modern Bayesian statistical modelling. Roberts' work involves explorations of the mathematical foundations of computational algorithms, and it combines both a deep theoretical understanding with a keen sense of the way such results can be used to guide and enhance practical applications.
Gero Friesecke works in applied analysis, on problems motivated by quantum mechanics and materials science, bringing rigorous techniques of mathematical analysis to bear on them. His interests range from classical problems on the stability of molecules to modern developments in quasicrystal structure in alloys.
Jonathan Tawn is a statistician whose research in environmental modelling studies the prediction of extreme events. He works closely with environmental scientists and engineers to ensure that frontline statistical research is available to decision-makers. The practical impact of his work is founded on his theoretical advances in the understanding of multivariate extreme statistics, and he combines mathematical power and innovation with leadership in the real-world implementation of these ideas.
Oliver Penrose was Professor of Mathematics at Heriot-Watt University until his notional retirement in 1994. He has remained active in research, principally in the area of statistical mechanics, and in the study of phase transitions. He combines his research work in mathematical physics with more metaphysical interests in the direction of time and the interpretation of quantum mechanics.
Paul Glendinning is Professor of Applied Mathematics at the University of Manchester Institute of Science and Technology (UMIST). His research interests are in dynamical systems, models of the time-evolution of complex mathematical or physical processes. Paul Glendinning uses a deft combination of rigorous analysis, geometry and penetrating intuition to discover the key features of dynamical systems, and to describe their evolution. His work is concerned both with the frequently surprising and intricate mathematical properties of dynamical systems, and with their interpretation for applications to physical processes.
Peter Donnelly is Professor of Statistical Science at Oxford University. His main research interests are in the application of probability and statistics to genetics, where theoretical and practical advances in probability modelling are applied to the understanding of evolutionary history and the structure of the human genome. His work combines stochastic processes and computationally intensive statistics, and involves extensive collaborations with biologists to develop new methodologies in genetics.
Shahn Majid's research explores the world of quantum geometry, on the frontier between pure mathematics and the foundations of theoretical physics. He uses mathematical structures from algebra and category theory to develop ideas concerning the structure of space and time. His research philosophy drives a search for the right mathematical language for a unified expression for the ideas of quantum physics, founded on the notion of non-commutative geometry
Michael Atiyah has made fundamental contributions to many areas of mathematics, but especially to topology, geometry and analysis. From his first major contribution -- topological K-theory - to his more recent work on quantum field theory, Atiyah has been influential in the development of new theoretical tools and has supplied far-reaching insights. He is a notable collaborator, with his name linked with other oustanding mathematcians through their joint research. He was awarded a Fields Medal in 1966, has been President of the Royal Society and Master of Trinity College, Cambridge. Atiyah has been the recipient of many honours and awards, including a a knighthood in 1983 and the Order of Merit in 1992.
Timothy Gowers is the Rouse Ball Professor of Mathematics at Cambridge University. He works in combinatorics, combinatorial number theory, and in the theory of Banach spaces, and has made fundamental contributions to these fields. He has solved many important problems on the structure of Banach spaces, and in combinatorics he has worked on difficult problems involving randomness and regularity in number theory. His exceptional insight and clarity have led to remarkable advances in these theories, arrived at by novel and creative combinations of analytic techniques and combinatorial ingenuity. His achievements were recognised in 1998 by the award of a Fields Medal (in mathematics, the equivalent of a Nobel Prize).
Tony Scholl does research in arithmetic algebraic geometry. This subject has its roots in classical problems in number theory, which are often easy to formulate but have proved very difficult to solve. Number-theory problems can often be rephrased in terms of geometry, and the subtleties of the resulting geometric structures explored by algebraic means. Tony Scholl has made profound contributions to this research programme, particularly in the theory of L-functions and modular forms.
Ulrike Tillmann works in algebraic topology, where her work combines original thinking in homotopy theory with strong geometric insight to give new understanding of large classes of topological structures. She has developed new algebraic models for homotopy theory and so new frameworks for proving penetrating and definitive results. Her work is also related to modern developments in the physics of topological field theories.
Valerie Isham is a Professor in the Department of Statistical Science at University College London. Her research in applied probability involves the development and application of stochastic models. Her theoretical work contributes to the toolbox of tractable models available to an applied probabilist, and she is involved in interdisciplinary projects that apply such models to the physical and medical sciences.