My research is mainly focused on symplectic and contact geometry; a field of geometry involving spaces that relate to smooth topology, complex geometry, and mathematical physics. Much of my work uses cut-and-paste/surgery techniques from smooth topology as tools for studying the global geometry of symplectic/contact manifolds, which is fruitful since they are much more "floppy" than many related geometries. A favorite tool of mine is something called the h-principle, a general technique in which the flexibility of local geometric models can be used to completely untangle any global geometric phenomena. Other portions of my work explore how symplectic/contact topology interplays with geometric invariants, such as those coming from pseudo-holomorphic curves or constructible sheaves.
Graph Legendrians and SL2 local systems
Mirror symmetry for the trefoil knot
Existence of Liouville structures on cobordisms
Existence of overtwisted contact structures on high dimensional manifolds
A frontal view on Lefschetz fibrations I
Lagrangian Caps in High Dimensional Symplectic Manifolds
Loose Legendrian Knots