Infinitely many fillings through augmentations

Abstract: In 2020, a few groups of people proved that certain Legendrian links in R^3 have infinitely many exact Lagrangian fillings that are distinct under Hamiltonian isotopy. These groups (Casals-Gao, Gao-Shen-Wang, Casals-Zaslow) used a variety of approaches involving microlocal sheaf theory and cluster structures. I'll describe a different, Floer-theoretic approach to the same sort of result, using integer-valued augmentations of Legendrian contact homology, and I'll discuss some examples that are amenable to the Floerapproach but not (yet?) the other approaches. This is joint work with Roger Casals.

algebraic geometrycombinatoricsdifferential geometrygeometric topologyquantum algebrarepresentation theorysymplectic geometry

Audience: researchers in the topic

Legendrians, Cluster algebras, and Mirror symmetry

Series comments: Schedule
School: January 4–8, 2021
Conference: January 11–15, 2021