Rigidity in contact topology

Abstract

Legendrian links play a central role in low dimensional contact topology. A rigid theory uses invariants constructed via algebraic tools to distinguish Legendrian links. The most influential and powerful invariant is the Chekanov-Eliashberg differential graded algebra, which set apart the first non-classical Legendrian pair and stimulated many subsequent developments. The functor of points for the dga forms a moduli space which acquires algebraic structures and can be used to distinguish exact Lagrangian fillings. Such fillings are difficult to construct and to study, whereas the only known complete classification is the unique filling for Legendrian unknot. A folklore belief was that exact Lagrangian fillings might be scarce. In this talk, I will report a joint work with Roger Casals, where we applied techniques from contact topology, microlocal sheaf theory and cluster algebras to find the first examples of Legendrian links with infinitely many Lagrangian fillings.

Speaker

Dr. Honghao Gao is an Associate Professor at Yau Mathematical Sciences Center. He obtained his PhD from Northwestern University. His area of research is contact and symplectic topology, and their relations with knot theory, microlocal sheaf theory and cluster algebras.