GT seminar: "Audin's conjecture beyond vector spaces"

Abstract: The original conjecture of Audin, proved by Cieliebak-Mohnke, asserts that any Lagrangian torus in the symplectic vector space bounds a holomorphic disc of Maslov index 2. In this talk, we will show that the same conclusion holds for Lagrangian tori in low degree affine hypersurfaces in C^n. More precisely, we prove that any closed, oriented, aspherical Lagrangian submanifold in a Liouville manifold with finite first Gutt-Hutchings capacity bounds a holomorphic disc of Maslov index 2. The proof relies on three ingredients: Fukaya-Irie's de Rham model of algebraic string topology, Cohen-Ganatra's idea in the construction of the Cieliebak-Latschev map, and Irie's technique of finite energy approximation of virtual fundamental chains.

This is a talk in our geometry and topology seminar series.