My interest is broadly in functional analytic methods for infinite-dimensional dynamical systems. Currently I study well-posedness and dynamics of various classes of abstract delay equations via dual semigroup theory. See my publications.
My motivation comes from within mathematics and from questions in mathematical biology and – more recently – control theory.
Delay equations is also the eponym of a domain that I have registered for the plan of creating a cooperative wiki about aspects of theory and examples of delay equations. If you would like to cooperate, let me know.