I will start by explaining the construction of a formal scheme starting with an integral affine manifold Q equipped with a decomposition into Delzant polytopes. This is a weaker and more elementary version of degenerations of abelian varieties originally constructed by Mumford. Then I will reinterpret this construction using the corresponding Lagrangian torus fibration X→Q and relative Floer theory of its canonical Lagrangian section. Finally, I will discuss a conjectural generalization of the story to decompositions of CY symplectic manifolds into symplectic log CY’s whose boundaries are ‘opened up’.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
