学术报告（高鸿灏 6.30）

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 is a moduli space which acquires algebraic structures and can distinguish exact Lagrangian fillings. Such fillings are difficult to construct and to study, whereas the only known 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.