Project Details
Description
Abstract
Award: DMS-0605097
Principal Investigator: Christopher Woodward
The PI will carry out research projects on the interplay of
holomorphic curves and two-dimensional gauge theory. With
K. Wehrheim and S. Mau the PI will study the role of Lagrangian
correspondences in Floer-Fukaya theory, and in particular prove
that the composition of functors associated to Lagrangian
correspondences is the functor associated to the composition. He
will also develop the mirror analogue of Horja's exact triangle.
He will apply these results to the construction of new invariants
of three and four-manifolds with boundary, possibly containing
tangles. With C. Teleman he will prove the Newstead-Ramanan
conjectures on Chern classes of the moduli space of bundles on a
curve and investigate K-theoretic Gromov-Witten invariants of
quotient stacks. With E. Gonzalez he will investigate
Gromov-Witten invariants for symplectic manifolds with
Hamiltonian group actions, generalizing the topological limit of
two-dimensional Yang-Mills theory. He will run several research
experiences for undergraduates, and improve the department's
undergraduate seminar program.
These projects will advance the understanding of symplectic
geometry, which is the mathematical language for classical
mechanics, and the relationship between category theory,
representation theory, and quantum physics. The research is also
expected to lead to advances in the theory of finite- and
infinite-dimensional Lie groups, which represent symmetries in
many areas of science.
Status | Finished |
---|---|
Effective start/end date | 7/1/06 → 12/31/12 |
Funding
- National Science Foundation: $326,954.00