Holomorphic Curves and Two-Dimensional Gauge Theory

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.

StatusFinished
Effective start/end date7/1/0612/31/12

Funding

  • National Science Foundation: $326,954.00

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