Symplectic geometry and Chern-Simons gauge theory
Principal Investigator: Lisa Jeffrey
Department: Computer & Mathematical Sciences
Grant Names: NSERC ; Discovery Grant ;
Award Years: 2016 to 2021
My research program is in symplectic geometry. It involves invariants in cohomology and equivariant cohomology. In some cases it also involves K-theory and equivariant K-theory of the based loop group, an infinite-dimensional analogue of a coadjoint orbit which arises in gauge theory. My research program involves conjugation spaces, which are symplectic manifolds equipped with an antisymplectic involution and a Hamiltonian torus action compatible with this involution. The based loop group is a conjugation space. Part of my research program involves Chern-Simons gauge theory, a topological field theory of 3-manifolds used to define invariants of 3-manifolds which do not depend on a choice of other structure such as a Riemannian metric.