Pure Mathematics

Fig5 steiner
Dynamical Systems A Steiner triple system on seven points

Research interests

Dynamical Systems:
Recent work has included constructing the moduli space of analytic unfoldings of parabolic maps; showing the rigidity of generic Darboux foliations; solving the tangential centre problem for hyperelliptic Hamiltonian systems and investigating the trigonometric moment problem via group theoretic computations. With our team of PhD students we are also investigating the bifurcation theory and analytic integrability of three dimensional Lotka-Volterra equations.

Graph Theory:
We study polynomial invariants of graphs, ribbon graphs, and knots.

Twistor Theory:
Our particular interest is in the geometrical and topological structures underlying the twistor description of space-time fields and their interactions.

Differential Algebra:
We are interested in various notions of integrability and study these by means of computer algebra. In particular, we have developed some methods for differential elimination.

Algebraic Systems Theory:
Systems of linear functional equations (such as linear control systems) allow a module-theoretic approach. We study such systems using algebraic analysis and homological algebra.

Moduli spaces in Geometry and Physics:
Moduli spaces are the geometric counterpart of parameter spaces. We are interested in the geometric properties of the spaces parametrising solutions of equations coming from Physics such as the Yang-Mills equations.

Our cover page shows an algebraic surface of degree 7, with 99 singularities, discovered by Oliver Labs in 2004. See