I'm particularly interested in global problems in geometry, specifically in symplectic geometry where many global problems live on a knife edge between "soft" (amenable to solution by an h-principle) and "hard" (displaying rigidity and requiring deep geometric techniques to tackle them). I like to study examples and concrete problems. My work to date falls into three main categories:

Lagrangian submanifolds in symplectic manifolds: Understanding their smooth and Hamiltonian knotting; understanding their 'quantum' invariants (i.e. holomorphic disc counts); in a given ambient space (like Del Pezzo surfaces or Cⁿ), classifying them or finding restrictions on their topology.

Holomorphic curves in symplectic manifolds: Calculating quantum cohomology rings and computing (family) Gromov-Witten invariants for specific non-Kaehler examples (twistor spaces and nilmanifolds); more generally, holomorphic curves arise as a tool in everything I do.

Symplectomorphism groups: Computing their homotopy groups; trying to understand their classifying spaces in terms of spaces of almost complex structures and in terms of moduli spaces of projective varieties.