I will describe a generalization of toric symplectic geometry to a new class of Poisson manifolds which are
symplectic away from a collection of hypersurfaces forming a normal crossing configuration. Using a "tropical
moment map", I will describe the classification of such manifolds in terms of decorated log affine polytopes,
in analogy with the Delzant classification of toric symplectic manifolds.
- Geometry and Analysis Seminar