Abstract: Knots are loops in Euclidean 3 space. On top of that, Legendrian knots additionally satisfy a particular differential equation, imposing constraints to the tangent direction at a certain point. Understanding Legendrian knots is one of the central topics in a subject called contact topology. In this pretalk, we will explain how to describe Legendrian knots through (a lot of) pictures, and introduce some algebraic invariants that are used to study Legendrian knots.

Abstract: Lagrangian fillings are surfaces bounding Legendrian knots, which live in a 4-dimensional space called symplectization. Different Lagrangian fillings can be distinguished by cluster charts in a moduli space associated to the Legendrian knots. In this talk, I will explain the joint work with Roger Casals, on how to construct a Lagrangian filling from a given cluster chart.