A quantitative look at Lagrangian cobordisms

Augmentations and Legendrians at the IAS
Topic:A quantitative look at Lagrangian cobordisms
Speaker:Lisa Traynor
Affiliation:Bryn Mawr College
Date:Friday, February 12
Time/Room:2:30pm - 3:30pm/S-101
Video Link:https://video.ias.edu/augmentslegends/2016/0212-Traynor

Lagrangian cobordisms between Legendrian submanifolds arise in Relative Symplectic Field Theory. In recent years, there has been much progress on answering qualitative questions such as: For a fixed pair of Legendrians, does there exist a Lagrangian cobordism? I will address two quantitative questions about Lagrangian cobordisms: For a fixed pair of Legendrians, what is the minimal "length" of a Lagrangian cobordism? What is the relative Gromov width of a Lagrangian cobordism? Regarding length, I will give examples of pairs of Legendrians where Lagrangian cobordisms are flexible in that the non-cylindrical region can be arbitrarily short; I will also give examples of other pairs of Legendrians where Lagrangian cobordisms are rigid in that there is a positive lower bound to their length. For the second quantitative measure, I will give some calculations and estimates of the relative Gromov width of particular Lagrangian cobordisms. This is joint work with Joshua M. Sabloff.