Ilia Zharkov: Immersed spheres in phase tropical hypersurfaces

Abstract: Phase tropical varieties are enhancements of tropical ones by adding coamoebas as fibers. With G. Kerr we showed that a phase tropical hypersurface is homeomorphic to the corresponding complex one. Thus one can pull back all the structure (smooth, complex, symplectic, etc) from complex hypersurface to the phase tropical. I will describe certain immersed "Langranian type" spheres as potential object of the Fukaya category.