My main research interests can be described as a mixture of partial differential equations, dynamical systems, and topology. An overall theme in this are variational methods. Concerning partial differential equations one subject deals with the relation between the topology of braids and the solutions of various types for second order scalar nonlinear diffusion equations. Related to this is Conley index theory. Recently I have become interested in the computational aspects of the Conley index, in particular with respect to braids as described above. Another subject is Hamiltonian systems and Floer homology. In this setting I am interested in generalizations of braid invariants. Related to this is the question of closed characteristics on non-compact energy manifolds.