I am happy to supervise across a range of themes broadly focussed on nontrivial questions in dynamical systems. The approaches can be both algebraic (for example involving the study of polynomial equations, or using exterior algebra); and geometric (for example involving partial orders and convex geometry).
I am also happy to supervise projects in related areas of pure mathematics.
• Some theorems which establish existence or nonexistence of limit cycles in the plane
• Graph theoretic approaches to the injectivity of functions
• Exterior algebra, compound matrices and their use in dynamical systems
• Know your limits: a study into the structure of limit sets in discrete-time dynamical systems
• Graphs and networks in biology
• Modelling chemical reaction networks
• On the maximal complexity of odd graphs
• A review of the Riemann and Lebesgue integrals and their inverse operation
• Asymptotic behaviour and bifurcation in biological models
• The beauty of chaos: a study in discrete and chaotic dynamical systems
• Networks, graphs and matrices