Results on Lagrangian fillings of Legendrian links

An important problem in contact topology is to understand Legendrian submanifolds; these submanifolds are always tangent to the plane field given by the contact structure. Legendrian links can also arise as the boundary of exact Lagrangian surfaces in the standard symplectic 4-ball. Such surfaces are called fillings of the link. In the last decade, our understanding of the moduli space of fillings for various families of Legendrians has greatly improved thanks to tools from sheaf theory, Floer theory and cluster algebras. One way to distinguish exact Lagrangian polytopes is by considering Newton polytopes of augmentations. We will discuss properties of Newton polytopes arising from Lagrangian fillings.

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https://sites.google.com/view/orsola-capovilla-searle/