Cohomology in algebra, geometry, physicsand statistics

Legendrian Isotopy from a Quantitative Viewpoint

We use techniques from persistence homology applied to the Chekanov-Eliashberg algebra in order to obtain a restriction on the oscillatory norm of a contact Hamiltonian that displaces a Legendrian in the contact vector space from its image under the Reeb flow. These techniques are also used to show that a Legendrian which admits an augmentation cannot C0-approximate a loose Legendrian, and to obstruct the existence of small positive Legendrian loops. This is joint work with M. Sullivan.