Alberto Baider and Richard Churchill will continue their research related to the dynamics of Hamiltonian systems. These are systems of differential equations of physical significance. This will involve the translation of much analysis into geometry and promises to have significant consequences in algebraic geometry. They intend to put Ziglin's non-integrability theorem in a geometric setting. In particular this project will relate the monodromy of the variational equations to the monodromy on the natural bundle of the varieties arising from the existence of certain integrals.
