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.