New Algebraic Invariants of Legendrian Links - Lenhard Ng 

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Topic: New Algebraic Invariants of Legendrian Links
Speaker: Lenhard Ng
Affiliation: Duke University
Date: May 24, 2024
For the past 25 years, Legendrian contact homology has played a key role in contact topology. I'll discuss a package of new invariants for Legendrian knots and links that builds on Legendrian contact homology and is derived from rational symplectic field theory. This includes a Poisson bracket on Legendrian contact homology and a symplectic structure on augmentation varieties. Time permitting, I'll also describe an unexpected connection to cluster theory for a family of Legendrian links associated to positive braids. Parts of this are joint work in progress with Roger Casals, Honghao Gao, Linhui Shen, and Daping Weng.