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.
