Thesis Defense: "On the Limiting Behavior of Variations of Hodge Structures"

Abstract: In this dissertation we will address three results concerning the limiting behavior of variations of Hodge structures. The first chapter introduces the main concepts involved and fixes some notation. In chapter two we discuss extensions classes representing LMHS, compute them for a class of toric families and introduce an alternative method for the computation of VHS arising from middle convolution. The next chapter is concerned with the so called Ap\'ery constants, we provide a method of computing such constants by using higher normal functions coming from geometry. Finally, in the last chapter we analyze a family of surfaces with geometric monodromy group $G_2$, and discuss the generic global Torelli theorem for such family.

Advisor: Matt Kerr