# Lisa Jeffrey

**E-mail: **jeffrey@math.toronto.edu

<>Office: Bahen Centre (BCIT) 6211 (St George); S 504C (UTSC)

**Office Phone:**978-5142 (St George); 287-7265 (UTSC)

**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
recent 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 Curriculum Vitae

To Papers and Publications

To Univ. of Toronto Department of
Mathematics

### Teaching

In Spring 2012 I taught MAT1312F.
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 fall 2014 I am teaching MATC63 (Differential Geometry).
To Course webpage for
MATC63

Last changed
January 8, 2014