Lekili's main area of research is symplectic topology and its applications to low dimensional topology. He is also interested in connections between symplectic topology and algebraic geometry and geometric representation theory.
Symplectic topology is concerned with the global topology of symplectic manifolds, a class of spaces that appeared first in classical mechanics. Over the past decades, symplectic geometry evolved from its roots in Hamiltonian mechanics into a branch of topology targeting global problems. Due to its relevance to string theory, the field has witnessed an explosion of activity in recent years, and many of the open questions currently under investigation by symplectic topologists have their origins in predictions made by theoretical physicists. Part of Lekili's research is motivated by a set of such predictions which goes by the name of the "mirror symmetry conjecture".
Lekili's personal web page can be found at