Mike Sullivan (UMass): Some quantitative results for Legendrian knots and submanifolds.

Abstract: Legendrians submanifolds of contact manifolds lie on both sides of the flexible/rigid divide in contact topology/geometry. I'll discuss results on the rigid side, which mostly rely on the barcodes (persistence) of various Floer-type pseudo-holomorphic curve theories associated to Legendrians. This includes: non-degeneracy of the Shelukhin-Hofer metric, C^0-closure, displacement energy bounds, existence of Reeb chords, flats in the group of contactomoprhisms, etc. I'll start with the definitions. This is old and new work, all joint with Georgios Dimitroglou Rizell.