URegina Topology and Geometry Seminar: Derek Krepski

Bundle gerbes on a manifold M provide geometric realizations of degree 3 cohomology classes of M. The space of infinitesimal symmetries of a bundle gerbe naturally carries the structure of a Lie 2-algebra, a deformation of the notion of Lie algebra where the Jacobi identity only holds 'up to homotopy’. This Lie 2-algebra of symmetries is related to other Lie 2-algebras associated to a closed differential 3-form, when the 3-form encodes the ‘higher curvature’ of the bundle gerbe - namely, the Poisson Lie 2-algebra of observables, and the Lie 2-algebra of sections of an exact Courant algebroid. This talk review the notion of bundle gerbe, and discusses the relations between the aforementioned Lie 2-algebras.