Research in the School is undertaken in a wide variety of areas of the mathematical sciences, including pure, applied, statistics, operational research as well as mathematical physics. The research environment is enhanced by the International Centre for Mathematical Sciences and by close collaboration with Heriot-Watt University through the Maxwell Institute which was set up in 2005 following significant funding from the Scottish Funding Council. Researchers in areas of applied mathematics benefit from the proximity of strong research groups elsewhere in the University and from collaborative opportunities with local companies and other users of research.
Research in Algebra and Number Theory in Edinburgh focuses on the following topics: Noncommutative Ring Theory, Representation Theory, Noncommutative Algebraic Geometry, Number Theory, and Commutative Algebra. There are close links in our work with other areas of research, with Geometry and Topology and with Mathematical Physics.
We work in a wide range of areas including Linear and Nonlinear Elliptic and Hyperbolic PDEs, Harmonic Analysis, Spectral Theory, Stochastic Analysis and Dynamical Systems. Analysis is part of the Pure Mathematics group at Edinburgh which has consistently been placed in the top 5 UK departments.
Research interests within the group include stellar dynamics, astronomical fluid dynamics, multiscale modelling and analysis, molecular dynamics, mathematical meteorology, Hamiltonian dynamics, nonlinear waves in fluids and solids, unsteady free boundary problems, optoelectronics, signal processing, exponential asympotics and homogenisation theory.
The Geometry and Topology group have interests in Differential and Algebraic Geometry, Algebraic and Geometric Topology, Twistor Theory and Integrable Systems.
We are the University of Edinburgh branch of the EMPG: a group of researchers with interests in Mathematical Physics, based at Edinburgh and Heriot-Watt universities. Our areas of interest include: String Theory, Supergravity, Conformal Field Theory, Integrability, Gauge Theory, Geometry of Supersymmetry, Quantum Gravity, Cosmology.
The main focus of the group is on mathematical and computing aspects of optimization. The core technology in optimization is the solution of large sparse linear and quadratic problems. We have world class expertise in the two main solution methods for these: the simplex method and the interior point method. In addition we have interests in global optimization, decomposition methods, parallel computing, industrial applications of optimization, and stochastic optimization.
The research interests of the Probability and Stochastic Analysis group focus on the following themes: Stochastic Differential Equations and Stochastic PDEs, Nonlinear Filtering and Stochastic Control; Applications of Stochastic Analysis in Mathematical Finance; Numerical Analysis of PDEs, Stochastic PDEs and Stochastic Differential Equations.
The methodological research of the group is Bayesian in nature. Areas of research include hierarchical multivariate random effects models, wavelets, nonparametric regression and resampling. There is a strong interest in applications with specific areas being forensic science, the law, agriculture, and functional genomics data such as gene expression microarrays.
