RESEARCH IN MATHEMATICS
Research Interests of Staff Members
To find more about the research groups in the Mathematics Department, please click here.
Analysis
- Dr Bonnington Clarke: Hyperbolic partial differential equations, control theory, boundary controllability and observability of linear systems of partial differential equations, hyperbolic differential boundary equations.
- Associate Professor Xuan Duong: Singular integrals, functional calculi, Hardy spaces and partial differential equations, harmonic analysis and partial differential equations.
- Dr Christopher Meaney: Harmonic analysis on Lie groups and symmetric spaces.
Category Theory
- Dr Michael Batanin: High dimensional category theory and higher dimensional homological algebra with applications to homotopy theory, algebraic topology, deformation theory and combinatorics.
- Dr Alexei Davydov: Category theory (monoidal categories), representation theory (representations and character tables of finite groups), mathematical physics, algebraic topology and algebraic K-theory.
- Dr Thorsten Palm: Higher dimensional categories.
- Dr Simona Paoli: Category theory, algebraic topology.
- Professor Ross Street: Category theory and its application to algebraic topology, homotopy theory, knots, combinatorics, group representations and computer science.
- Dr Mark Weber: Higher dimensional category theory, homotopy theory, combinatorics, logic.
- Professor Michael Johnson (Department of Computing): Category theory, applications to computer science, homotopy theory and universal algebra.
- Associate Professor Dominic Verity (Department of Computing): Higher-dimensional category theory and its applications to simplicial/cubical geometries, homotopy theory, non-abelian cohomology, category theory and sheaf representations of rings.
Number Theory and its Applications
- Professor William Chen: Uniform distribution, discrepancy theory and analytic number theory.
- Dr Gerry Myerson: Number theory, finite fields, multivariate polynomials, uniform distribution, Dedekind sums, covering congruences and magic squares.
- Emeritus Professor Alf van der Poorten: Number theory, theory of functions, p-adic analysis, transcendence theory, diophantine approximation, diophantine equations, application of computers in number theory, approximation of functions, value distribution of functions and p-adic methods in number theory.
- Dr Rodney Yager: Algebraic number theory, arithmetic of elliptic curves, abelian varieties, Iwasawa theory, p-adic L-functions and their relationship to arithmetic properties of the associated variety.
- Professor Igor Shparlinski (Department of Computing): Analytic and computational number theory, finite fields, application of number theory to computer science and to the complexity of computations.
Mechanics, Geometry, Waves and Nonlinear Dynamics
- Dr Salah Mehanee: Multi-dimensional modelling and inversion of geophysical techniques with emphasis on electromagnetic methods.
- Dr Sergey Panin: Analytical-numerical techniques based on analytical regularization and their implementation in acoustic and electromagnetic theory.
- Dr Tanya Schmah: Geometric mechanics and symmetry, sympletic and Poisson geometry, non-linear dynamics.
- Professor Paul Smith: Geometric mechanics and symmetry. Mathematical modelling of acoustic and electromagnetic waves, analytical and computational methods, nonlinear dynamics in electronic systems. Ordinary and partial differential equations, integral equations.
- Dr Elena Vinogradova: Mathematical modelling of acoustic and electromagnetic wave diffraction, potential theory problems, analytical and numerical techniques, applications to resonant phenomena, antenna design, radar cross section. Direct and inverse scattering problems. Integral and series equations, ordinary and partial differential equations, special functions and integral transforms. Electronic systems models and nonlinear dynamical systems.
Mathematical Physics
- Senior Research Fellow Dr John Corbett: Mathematical and conceptual problems of quantum theories, quantum numbers, non-locality and measurement problem, tripartite entanglement, reconstruction problem, spatial toposes, and topos theory models of non-relativistic and relativistic quantum systems. The localisation in quantum space-time. General relativity.
- Dr Frank Valckenborgh: Lattice theory, projective geometry, category theory.
Algebraic Geometry, Mathematical Computing and Typesetting
- Dr Ross Moore: Algebraic geometry, mathematical computing, mathematical typesetting and electronic presentation. Cohomology of vector bundles over projective spaces, Horrocks-Mumford vector bundle. Mathematical computer graphics, computational number theory, chaos, tilings and curves.