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.

Some videos:

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