Lisa Jeffrey

Lisa Jeffrey
Name	Lisa Jeffrey
Birth date	1960s
Birth place	Toronto, Ontario, Canada
Fields	Mathematics
Workplaces	Columbia University; Princeton University; Courant Institute; University of Toronto; Mathematical Sciences Research Institute
Alma mater	University of Toronto; Harvard University
Doctoral advisor	Raoul Bott
Known for	Symplectic geometry; geometric representation theory; equivariant cohomology
Awards	Sloan Research Fellowship; AMS Fellowship; Simons Fellowship

Lisa Jeffrey Lisa Jeffrey is a Canadian-American mathematician noted for contributions to symplectic geometry, geometric representation theory, and the topology of moduli spaces. Her work connects techniques from differential geometry, algebraic topology, and mathematical physics, influencing research related to gauge theory, moduli of flat connections, and equivariant localization. Jeffrey has held faculty positions at leading institutions and has directed programs at major research centers.

Early life and education

Jeffrey was born in Toronto and completed undergraduate studies at the University of Toronto, where she studied with exposure to faculty in topology and geometry such as John Conway (as visitor lecturers) and contemporaries in the Canadian mathematical community. She pursued graduate studies at Harvard University, earning a Ph.D. under the supervision of Raoul Bott with a dissertation that developed analytical and topological methods for spaces arising in gauge theory and symplectic reduction. During her doctoral and postdoctoral years she held appointments and visiting positions at institutions including the Institute for Advanced Study, the Mathematical Sciences Research Institute, and the Courant Institute of Mathematical Sciences.

Research and mathematical contributions

Jeffrey's research centers on symplectic geometry and the topology of moduli spaces arising from gauge theory and representation varieties. She made foundational contributions to the study of symplectic reduction and the cohomology of moduli spaces of flat connections on Riemann surfaces, linking techniques from equivariant cohomology, Morse theory, and localization formulas. Her work often interacts with the Atiyah–Bott framework on Yang–Mills moduli spaces and connects with results by Michael Atiyah, Raoul Bott, and Edward Witten on moduli of vector bundles and quantum field theoretic approaches.

Key results include rigorous formulations of nonabelian localization principles and computations of intersection pairings on moduli spaces that built on the work of Witten on two-dimensional gauge theory and the Verlinde formula. Jeffrey developed analytic methods to study symplectic quotients and the behavior of reduced spaces under group actions, relating to contributions by Kirillov, Berline-Vergne, and Duistermaat-Heckman. Her research also interfaces with geometric representation theory topics treated by George Lusztig, Bertram Kostant, and Nicholas M. Katz in the study of character varieties and representation spaces for surface groups and compact Lie groups.

Her collaborations span interactions with researchers in mathematical physics, including work addressing moduli spaces relevant to topological quantum field theory and connections with the mathematical structures used in the study of conformal field theory and knot invariants developed by Vladimir Drinfeld, Edward Frenkel, and Graeme Segal.

Academic career and positions

Jeffrey has held faculty appointments at the University of Toronto and at Columbia University, and has been affiliated with the Courant Institute of Mathematical Sciences at New York University and the Institute for Advanced Study in Princeton, New Jersey. She served as a visiting scholar and program organizer at the Mathematical Sciences Research Institute in Berkeley, California and has lectured widely at conferences organized by the American Mathematical Society, the International Congress of Mathematicians, and the Society for Industrial and Applied Mathematics.

In administrative and leadership roles, Jeffrey has been involved in directing graduate programs and research seminars, supervising doctoral students and postdoctoral fellows who later held positions at institutions such as University of Michigan, Stanford University, and University of Chicago. She has been active in organizing workshops on symplectic geometry, moduli spaces, and mathematical aspects of quantum field theory at venues including the Banff International Research Station and the Centre International de Rencontres Mathématiques.

Awards and honors

Jeffrey has received recognition for her contributions to geometry and topology, including a Sloan Research Fellowship early in her career and later election as a fellow of the American Mathematical Society. She has been awarded research fellowships from organizations such as the Simons Foundation and has been invited to give plenary and invited addresses at meetings of the Canadian Mathematical Society and the European Mathematical Society. Her leadership in organizing influential programs has been acknowledged by selections to advisory panels at the National Science Foundation and other funding agencies.

Selected publications and lectures

Jeffrey's publications include influential articles on symplectic reduction, moduli spaces of flat connections, and nonabelian localization. Representative works include papers that apply equivariant cohomology and localization to compute intersection pairings on moduli spaces, contributions to conference proceedings on gauge theory and geometry, and lecture notes from advanced graduate courses and summer schools. Her invited lectures and addresses have been delivered at venues such as the International Congress of Mathematicians, the Institute for Advanced Study, the Mathematical Sciences Research Institute, and the Banff International Research Station. Numerous collaborations appear in journals published by the American Mathematical Society and in proceedings of the Symposium on Geometry and Physics.

Category:Canadian mathematicians Category:Symplectic geometers