Colin Diemer: Secondary Stacks and Toric Moduli
Equivariant degenerations of polarized toric varieties are parametrized by an object known as the secondary polytope. Its low dimensional strata are explicitly describable. We discuss the use of this space for understanding topological and symplectic monodromy of toric hypersurfaces. This involves imposing a certain natural stack structure on the secondary polytope, and understanding the appearance of vanishing cycles via a tropical Morse theory. This is part of a joint work with L. Katzarkov and G. Kerr.