Consider a Lagrangian torus fibration à la SYZ over a non-compact base. Using techniques from this arXiv paper, I will discuss the construction of wrapped Floer theory in this setting. Note that this setting is generally not exact even near infinity. The construction allows the formulation of a version of the homological mirror symmetry conjecture for open manifolds which are not exact near infinity. According to time constraints, I will apply this to prove homological mirror symmetry in the case where the A-model is the complement of an anti-canonical divisor in a toric Calabi Yau manifold.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
