Speaker: Gabe Kerr (KSU)

Abstract: In this talk, I will give the definition of the phase tropical hypersurface arising from a polytope with a coherent triangulation. This is a topological version of a singular integrable system. I will discuss aspects of a joint work with I. Zharkov which proved that there is a homeomorphism between the phase tropical hypersurface and a complex hypersurface (this is known as Viro's Conjecture). With this, Mikhalkin's pair of pants decomposition of a complex hypersurface becomes a polyhedral decomposition and several Lagrangians arising in mirror symmetry have conjectural accompanying decompositions which are well controlled topologically. I will discuss these subcomplexes and evidence of their mirrors in matrix factorizations. This is joint work with I. Zharkov.