A Local Quasimorphism Property for Link Spectral Invariants

Watch this 22-minute lecture from the Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar where Ibrahim Trifa from ETH Zurich explores the local quasimorphism property for link spectral invariants. Discover how these invariants are defined for finite collections of disjoint Lagrangian circles on symplectic surfaces with specific area constraints, using Lagrangian Floer homology of the product of circles inside the symmetric product of the surface. Learn why these spectral invariants behave as quasimorphisms on spherical surfaces but not on higher genus surfaces, and understand Trifa's demonstration that link spectral invariants on higher genus surfaces are local quasimorphisms when restricted to Hamiltonian diffeomorphisms supported in topological discs. This presentation covers joint work with Cheuk Yu Mak, scheduled for April 11, 2025.