Computational Topology in Dynamical Systems: Conley Index Theory, Set Oriented Numerics, computational aspects of Morse/Floer theory, and Applications.
• A Posteriori Analysis and Numerics in Dynamical Systems: Parameterization of invariant manifolds with rigorous error bounds. Applications to computer assisted proof of connecting dynamics for diffeomorphisms, ordinary and partial differential equations.
• KAM Theory: existence and numerical approximation of invariant manifolds in spite of small divisors.