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
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.

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.

To Curriculum Vitae
To Papers and Publications
To Univ. of Toronto Department of Mathematics

Teaching

In Fall 2006 I am teaching MATB44.

To Course webpage for MATB44
In Fall 2006 I am teaching MAT1300Y. To Course webpage for MAT1300
In Winter 2007 I am teaching MATC46. To Course webpage for MATC46

(This page is under construction) February 12, 2007