Dan Xie: One classification of theories with eight supercharges

Abstract. We will discuss the classification of theories with eight supercharges by using the associated Coulomb branch geometry,which is described by a mixed Hodge module over Coulomb branch. The classification of rank one case is related to classification of rational elliptic surface,and the rank two is related to genus two Lefchetz fibration over P^1. Arithmetic aspects such as Mordeil-Weil lattice would also play an important role.