2017 Lecturer: Lisa Jeffrey
Real loci in symplectic manifolds
Let M be a symplectic manifold and let σ be an antisymplectic involution on M. The real locus is the fixed point set of the involution. It is a Lagrangian submanifold. Suppose also M is equipped with the Hamiltonian action of a torus T. It is possible to define a compatibility between T and M. This set of ideas was introduced in a 1983 paper by Hans Duistermaat. In this talk I will describe some developments in this field since Duistermaat’s foundational paper. My contributions in this area are joint work with Liviu Mare, and (in a separate project) with Nan-Kuo Ho, Khoa Dang Nguyen and Eugene Xia.
Jeffrey is a Professor of Mathematics at the University of Toronto, where she has been on the faculty since 1998. Before that, she held an Assistant Professorship at Princeton University, followed by an Assistant Professorship at McGill University. Jeffrey received her DPhil from Oxford University in 1992, under the supervision of Michael Atiyah. The work of her thesis provided mathematically rigorous proofs of conjectured statements about three-manifold invariants connected with quantum field theory.
Jeffrey is best known for her joint work with Frances Kirwan on localization and moduli spaces. They determined the structure of the cohomology ring of the moduli space of representations of the fundamental group of a surface. This was an application of their earlier work, developed to study the cohomology rings of symplectic quotients. More recently, Jeffrey’s work has been focused on the based loop group in K-theory. In joint work with Harada, Holm, and Mare, she showed the connectedness of the level sets of the moment map on the based loop group.
Professor Jeffrey has been an active mentor during her years at Toronto. Eleven students have obtained their PhDs under her guidance, and she is currently supervising six more. She has supported numerous postdoctoral fellows, and she has advised many undergraduates and Masters students in thesis and reading projects.