Introduction to Lagrangian Fillings of Legendrian Links - Part 1

Explore an in-depth introduction to Lagrangian fillings of Legendrian links in this first talk of a series. Delve into the geometric context for studying Legendrian links and their Lagrangian fillings, examining various construction methods and techniques for distinguishing Hamiltonian isotopy classes. Discover how this perspective naturally leads to cluster algebras and learn about the main theorem connecting cluster algebras and Lagrangian fillings. Begin to unpack the key ingredients necessary for proving this theorem. Address intriguing questions about the decomposability of exact Lagrangians, the basis formation of γ_i for H_i(L), and the possibility of finding minimal generators of Y-trees that generate H_1 of the Lagrangian filling.