Mathematics
Group Members
Staff: Prof. Simon Cox, Prof. John Gough, Prof. Vass C. Mavron, Prof. Gennady Mishuris, Dr Dave Binding, Dr Daniel Burgarth, Dr I. Tudur Davies, Dr Robert J. Douglas, Dr D. Gwion Evans, Dr Rolf Gohm, Dr Tom McDonough, Dr Adil Mughal
Research Assistants: Dr Claus Koestler, Dr Michal Wrobel
PhD Students: Christiana Andreou, David Ferguson, Piotr Kusmierczyk, Monika Perkoska, Lewis Pryce, Adam Vellender and Sebastian Wildfeuer
Recent mathematics publications
Overview
Mathematics is the basic language of the modern technological world: an understanding of Mathematics is essential for studying and formulating technical issues, and the application of Mathematics to Physical and Engineering modelling and problem solving remains of paramount importance. Research interests in Mathematics cover a broad field of pure and applied mathematics. This includes mathematical modelling of solids and structures, rheology of complex fluids and foams, analysis and measure theory, functional analysis, operator algebras, open quantum systems and algebraic combinatorics. We have active research links internationally with both mathematicians and users of mathematics, involving areas of mathematical modelling, quantum engineering, industrial mathematics, coding theory and mathematical physics.
Algebraic Combinatorics
This group is active in design theory, coding theory and the representation theory of Weyl groups and associated Hecke algebras. Work in design theory is currently concentrated on quasi-symmetric designs and Hadamard designs; work in coding theory deals with those error-correcting linear codes which are associated with geometric designs, particularly affine and projective planes and spaces; and work on representation theory is mainly concerned with the Kazhdan-Lusztig representations of the symmetric group and the associated Kazhdan-Lusztig cells.
Mathematical Modelling of Structures, Solids and Fluids
The group's interests cover diverse problems in solid and fluid mechanics, rheology and meteorology. They include elasticity and related multiphysics problems; biomechanics; transmission problems in non-smooth domains; spectral and scattering problems for periodic structures with defects; plasticity and viscoplasticity; flow behaviour of elastico-viscous liquids, including polymer solutions; the structure and dynamics of foams and related materials; linear analysis of complex fluids; optimal mass transfer problems and their applications; measure theory and convex analysis. Our approaches include modelling, accurate mathematical analysis, numerical simulation and experiment.
Quantum Structures, Information and Control
This group works in the area of quantum structures and their applications. Specific interest lies in systems that interact with their environment, and in particular the emergent field of quantum control engineering. This is a highly interdisciplinary field incorporating ideas from information theory, (non-commutative) stochastic analysis, mathematical physics for open quantum systems, and modern control theory. The group has an expertise in functional analysis and operator algebra theory, which it applies to practical quantum models.