Claremont Topology Seminar: Orsola Capovilla-Searle (UC Davis)

We welcome all undergraduate/graduate students and faculty to attend topology seminar!

Speaker: Orsola Capovilla-Searle (UC Davis)

Title: Exact Lagrangian fillings of Legendrian links

Abstract: 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 arise as wavefronts in optics, and can sometimes be used to distinguish contact structures. Legendrian links can also arise as the boundary of exact Lagrangian surfaces in the standard symplectic 4-ball which are called fillings of the link. In the last seven years, 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. I will talk about recent work establishing connections between fillings and Newton polytopes, as well as applications to higher dimensional Legendrian submanifolds and non-orientable fillings.