Arnol'd's Chord Conjecture for Conormal Legendrian Lifts

Explore Arnol'd's chord conjecture through this advanced mathematics lecture focusing on conormal Legendrian lifts in symplectic geometry. Delve into the theoretical foundations of the chord conjecture, originally proposed by Arnol'd for the standard contact three-sphere, which asserts the existence of a Reeb chord with boundary on every closed Legendrian submanifold of a closed contact manifold for every contact form. Examine how this conjecture has been established in various settings by mathematicians including Cieliebak, Mohnke, Hutchings, and Taubes. Learn about a proof of the chord conjecture specifically for conormal bundles of closed submanifolds of any closed manifold when viewed as Legendrians in the co-sphere bundle, which extends Grove's result in Riemannian geometry concerning the existence of geodesics normal to submanifolds. Discover how wrapped Floer cohomology with local coefficients serves as the primary method of proof in this collaborative research with Dylan Cant and Egor Shelukhin, presented as part of the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar series.