凯时kb88.comA filling is an oriented surface bounding a link. Lagrangian fillings can be constructed via local moves in finite steps, but it was unknown whether a Legendrian link could admit infinitely many Lagrangian fillings. In this talk, I will show that Legendrian torus links other than (2,m), (3,3), (3,4), (3,5) indeed have infinitely many fillings. These fillings are constructed using Legendrian loops, and proven to be distinct using the microlocal theory of sheaves and the theory of cluster algebras. This is a joint work with Roger Casals.