Lisa Jeffrey


<>Office: Bahen Centre (BCIT) 6211 (St George); IC474 (UTSC)
Office Phone:416-287-7265
Office FAX: (416) 978-4107

Research Interests

My current research uses techniques from pure mathematics (notably symplectic geometry, the natural mathematical framework for classical mechanics) to prove results obtained by theoretical physicists using the methods of quantum field theory. In my doctoral thesis (under the supervision of Michael Atiyah) I provided a mathematically rigorous proof of results on the asymptotics of the three-manifold invariants of Witten and Reshetikhin-Turaev which Witten had conjectured based on his approach to these invariants using quantum field theory.

In joint work with Frances Kirwan I have proved formulas of Witten which encode the structure of the cohomology ring of the moduli space of holomorphic vector bundles on a Riemann surface: the main technique used is a method from symplectic geometry and equivariant cohomology known as nonabelian localization, which Kirwan and I developed in our initial paper. Later developments are joint work with Young-Hoon Kiem, Frances Kirwan and Jonathan Woolf.

In joint work with Jonathan Weitsman I have studied these moduli spaces using techniques from symplectic geometry (the theory of Hamiltonian group actions): these methods endow the moduli spaces with Hamiltonian flows, in some cases leading to a structure of integrable system on them, and yielding a very transparent description of the formulas for their symplectic volumes.

In joint work with Megumi Harada, Tara Holm and Augustin-Liviu Mare, we have shown that the level sets of the moment map for the natural torus action on the based loop group are connected.

In joint work with Jacques Hurtubise and Reyer Sjamaar (following an earlier paper joint with Victor Guillemin and Reyer Sjamaar) we study imploded cross-sections. This is a refinement of the symplectic cross section.

To Univ. of Toronto Department of Mathematics


In winter 2021 I am teaching MATD34 (Complex Variables II, UTSC) To Course webpage for MATD34
In winter 2021 I am teaching MATD67 (Differentiable Manifolds, UTSC) To Course webpage for MATD67
In winter 2020 I am teaching MAT1312HS (Topics in Geometric Topology: Topology and Geometry of Torus Actions and Related Combinatorics) To Course webpage for MAT1312HS
In fall 2018 and fall 2019 I taught MATC34 (Complex Variables I) at University of Toronto Scarborough. To Course webpage for MATC34
In fall 2017, fall 2018 and fall 2019 I taught MATC63 (Differential Geometry) at University of Toronto Scarborough To Course webpage for MATC63
In fall 2016 I taught MAT1312F, Symplectic Geometry. (M 1-2 GB120, W 1-3 BA6180) To Course webpage for MAT1312
In Fall 2013 I taught MAT1300F. To Course webpage for MAT1300
In Winter 2014 I taught MATC46. To Course webpage for MATC46
In winter 2015 I taught MATD34 (Complex Variables II). To Course webpage for MATD34
e In winter 2015 I taught MAT1301 (Algebraic Topology). To Course webpage for MAT1301
In fall 2015 I taught MAB44 (Differential Equations I). To Course webpage for MATB44
In winter 2016 I taught MATC27 (Topology). To Course webpage for MATC27
In fall 2016 I am teaching MATC63 (Differential Geometry). To Course webpage for MATC63
See notes to MAT1300 (last taught fall 2013): Notes from MAT1300

Table of contents for notes to MAT1300: Notes from MAT1300

Last changed March 18, 2015