1. The development of "topological domain theory", a generalisation of the classical domain theory of Scott that includes a wider collection of topological spaces than usually considered. This feature allows topological domains to be closed under a wider collection of computationally important constructions than classical domains.
2. Establishing "synthetic domain theory" as the most powerful known approach to obtaining a general axiomatic account of domain-theoretic models.
3. Developing novel proof-theoretic methods for reasoning with inductive definitions based on using cyclic proofs by ~infinite descent~ rather than the standard proofs by induction.