Brunel University Random Systems Research Centre
The scientific objective of the centre is to investigate and develop the theory of random systems. By random systems we mean a broad variety of theoretical questions and applications. For example in Mathematical Physics random matrices describe the universal properties of many processes in nature, including quantum chromodynamics in high-energy physics, quantum chaos, the Riemann hypothesis in number theory and fluctuations in stock prizes in economics. In Graph theory polynomials, such as the Tutte Polynomial, link diverse areas such as statistical physics, random networks and knot theory. Complex networks have seen the emergence of new scale-free and small-world graphs. Joint graph theory/theoretical physics approaches may be used to develop the theory of their geometry and topology and to describe basic processes on them, such as diffusion, percolation, breakdown, conduction and transport. In Operational Research and Risk Modelling the emphasis is on finding such concepts in finance, in particular through the evaluation of risk. A list of our publications.
The research methodologies employed within BURSt include non-equilibrium statistical mechanics, matrix integrals, saddle-point techniques and orthogonal polynomials from mathematical and theoretical physics, graph polynomials, computational complexity and matroids from discrete mathematics and optimization methods and Bayesian networks from operational research. Within BURSt, there is a strong emphasis on analytical solutions and on the rigorous treatment of simply posed problems.
We are particular keen to make contact with potential students, research assistants or collaborators. If you are interested in our work please contact the member of BURSt with research interests closest to your own, or the BURSt Director, Professor Geoff Rodgers.
BURSt organise a series of Research Seminars and Workshops. Among other research networks BURSt is the home for NET-ACE a Marie Curie Early Stage Training Site, in which Marie Curie fellows study network theory and applications to finance, computing and engineering.
The BURSt Research Centre team work in three Research Groups
- Mathematical Physics Research Group research in the following areas: random matrix theory, non-equilibrium statistical mechanics applied to economics and social sciences, waves in disordered / chaotic systems and quantum chaos, quantum chromodynamics and high energy physics, integrable models and asymptotic analysis.
- Combinatorics Research Group research in the following areas: graph polynomials, polynomial inequalities, matroids, asymptotics of orthogonal polynomials and related determinants, frequency assignment problem and graph colouring.
- Operational Research and Risk Modelling Research Group research in the following areas: financial engineering: asset and liability management, enhanced indexation, index tracking, pricing; mathematical programming: linear, integer and stochastic programming; metaheuristics: population heuristics, tabu search, variable neighbourhood search; risk: especially within finance, value at risk.