Abstract

Log-symplectic structures are a type of Poisson structures that are symplectic outside of a hypersurface. The aim of this talk is to discuss whether the deformation theory of Lagrangian submanifolds in this setting is as well-behaved as in symplectic geometry. We will focus on deformations of a Lagrangian submanifold contained in the singular locus of a log-symplectic manifold. Using a normal form around the Lagrangian, we show that the deformation problem is governed by a DGLA. We discuss whether the Lagrangian admits deformations not contained in the singular locus, and we give criteria for unobstructedness. If time permits, we also address equivalences of Lagrangian deformations under Hamiltonian and Poisson isotopies. This is joint work with Marco Zambon.