Speaker: Ilia Zharkov (KSU)

Abstract: The complex pair-of-pants is a hypersurface in (C*)^n defined by the equation 1+z_1+. . .+z_n=0. It projects to the amoeba A in R^n and the coamoeba C in the torus T^n. The amoeba has a skeleton SkA, also known as the tropical hyperplane, and the coamoeba has a skeleton SkC, known as the boundary of the permutahedron. I will introduce a new object, the obertropical pair-of-pants, in SkA x SkC, which is isotopic to the original pair-of-pants and discuss its application for making the discriminant in a topological SYZ fibration to be of codimension 2. This is a joint project with H. Ruddat.