Mathematics

In this seminar, I will give the definitions of  "(1,2) Yukawa couplings" and of "Period Map" for a family of compact CY threefolds. I will start recalling, briefly, what is a Hodge structure of weight . Then, I will define the concept of "variation of Hodge structure": I will first present the case in which the variation is associated with a family of compact Kähler manifolds, and then I will give an intrinsic definition. Finally, I will present two important objects associated with a family of compact CY threefolds: the "(1,2) Yukawa coupling", and the "Period Map". Both these objects will play an important role in the formulation of the mirror symmetry conjecture.