Chain level string bracket and punctured holomorphic discs - Yin Li

Slides available here: https://www.math.stonybrook.edu/PDFs/...

Stony Brook Mathematics Colloquium
November 9, 2023

Yin Li, Columbia University

The original form of Audin's conjecture states that any Lagrangian torus in the symplectic vector space bounds a Maslov index 2 holomorphic disc. One way to prove this conjecture, due to Fukaya and Irie, is to relate the compactification of the moduli space of (perturbed) holomorphic discs to operations in string topology. In this talk, I will describe how to generalize their ideas to Liouville manifolds with finite first Gutt-Hutchings capacity (e.g. low degree affine hypersurfaces in C^n), and prove that any oriented aspherical Lagrangian submanifold in these Liouville manifolds bounds a pseudoholomorphic disc of Maslov index 2. To do this we will introduce some moduli spaces of punctured holomorphic discs and relate their compactifications to operations in string topology, in particular the chain level string bracket.