Lagrangian Fibrations in Symplectic Topology and Mirror Symmetry

Science / Mathematics

Symplectic geometry is rooted in the physical theory known as Hamiltonian mechanics. This relationship with physics has led to the mathematical concept of mirror symmetry, influenced by physical concepts in string theory. This concept bridges two distinct mathematical fields: algebraic geometry and symplectic geometry. Within this relationship, Lagrangian subvarieties serve as the core objects in the structure on the symplectic aspect. Weinstein’s credo that “everything is a Lagrangian subvariety,” underscores their significance, suggesting that all objects and constructions in symplectic geometry should be expressed as Lagrangian subvarieties.” Our project aims to explore the behavior of these Lagrangians in families, known as Lagrangian fibrations, their connections with Gromov-Witten theory, and the ambitious task of classifying them within a specific space.

Amount invested

R$ 100,000.00
  • Topics
  • Gromov-Witten theory
  • Hamiltonian mechanics
  • Symplectic geometry