Dr Rodney Halburd, PhD
EPSRC Advanced Research Fellow

Room 703
Tel:- 020-7679-2973
E-mail:- r.halburducl.ac.uk
Fax: 020-7383-5519

Research Interests
Integrable systems, complex analysis

One aspect of Dr Halburd's research concerns integrable systems. Roughly speaking, integrable systems are equations that are in some sense exactly solvable. Integrable equations, particularly soliton equations, appear in many applications from water waves (the Kortewegde Vries equation) to the theory of optical fibres (the nonlinear Schrödinger equation) to general relativity (the Ernst equation) to differential geometry (the self-dual Yang-Mills equations.) He studies integrable systems in the form of differential, discrete and ultra discrete equations. In particular, he uses tools from complex analysis (e.g. Nevanlinna theory) and number theory (e.g. height growth and Diophantine approximation) to classify integrable equations and describe some of their properties. In the case of equations with one independent variable, Dr Halburd is especially interested in the Painlevé equations and novel reductions of the self-dual Yang-Mills equations such as the Darboux-Halphen system. He also studies the singularity structure of solutions of differential equations. Other interests include general relativity.