Abstract:In this talk, we will concentrate on special case of algebraic varieties, smooth projective complete intersections. We will construct a special type of homotopy algebra, called the DGBV (differential Gerstenhaber Batalin-Vilkovisky) algebra associated to any smooth projective complete intersections X. This DGBV algebra gives a new way to compute the primitive middle dimension cohomology and the period integrals of X. Moreover, this construction is purley algebraic and algorithmic which is computable using a computer program. As an application, we get an explicit algorithm to compute the inverse value of the modular j-fuction. The talk is based on joint work with Jeehoon Park.