Lisa Jeffrey
n
E-mail: jeffrey@math.toronto.edu
<>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
Teaching
In winter 2022 I am teaching MAT1301 (Algebraic Topology).
To Course webpage for MAT1301
In winter 2022 I am teaching MATC63 (Differential Geometry).
To Course webpage for
MATC63
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