Project Grant 2152257

This $271,119 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research on complex Lagrangians, integrable systems, and quantization in relation to mirror symmetry. The University of California, Davis will lead a research group investigating mirror symmetry as it relates to symplectic geometry and complex algebraic geometry. The group will establish complex Lagrangian geometry as a tool to study geometric questions and quantization arising in modern geometry and topology. It will construct concrete models demonstrating aspects of mirror symmetry such as symplectic-complex algebraic duality, Langlands duality, the Laplace transform, and relations to three-manifold invariants. The group will also advance understanding of complex integrable systems and their quantum counterparts using Hitchin integrable systems. Workshops, summer schools, and conferences will disseminate results and train early career researchers, in line with NSF's broader impacts criteria.