|An example of a bipartite graph on a torus called a dimer model, together with its dual quiver.||Newton’s construction of a cubic through seven given points, one of which is a double point.|
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.
We study polynomial invariants of graphs, ribbon graphs, and knots.
Our particular interest is in the geometrical and topological structures underlying the twistor description of space-time fields and their interactions.
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