Research interests

My research interests are Symplectic Topology, Contact Topology, Dynamics, and Geometric Analysis.

More specifically I am interested in the metric and topological study of the spaces formed by the natural objects

in Symplectic and Contact Topology, such as Hamiltonian diffeomorphisms, contactomorphisms, strict

contactomorphisms and Lagrangian cobordisms. I am interested in various metric structures on these

spaces including Hofer's metric. Most recently I became involved in a revolution in quantitative symplectic topology related to the introduction of methods of persistent homology, originating in topological data analysis. These tools have proven useful in addressing various open questions in symplectic topology, and most recently, Hamiltonian dynamics. I am also working on the analysis of a natural variant of the Calabi-Yau equation for HKT manifolds.