Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

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 $X\rightarrow Q$ 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".