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 extension 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 Apery 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 G2, and discuss the generic global Torelli theorem for such a family.

Committee Chair

Matt Kerr

Committee Members

Charles Doran, John Shareshian, Roya Beheshti, Wushi Goldring,

Comments

Permanent URL: https://doi.org/10.7936/K7CR5RNR

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

Spring 5-15-2016

Language

English (en)

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Mathematics Commons

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