ORCID

0009-0000-6442-5153

Date of Award

5-8-2024

Author's School

Graduate School of Arts and Sciences

Author's Department

Mathematics

Degree Name

Doctor of Philosophy (PhD)

Degree Type

Dissertation

Abstract

Let $S$ be an arithmetic quotient of a Hermitian symmetric domain and $X/S$ be a family of varieties over $S$. One interesting problem is to find the Hodge classes of $X$, and if possible, to prove the Hodge conjecture for $X$. Using techniques from automorphic forms, we studied the Hodge conjecture for certain families of varieties over arithmetic quotients of balls and the Siegel domain of degree two. As a byproduct, we derived formulas for Hodge numbers in terms of automorphic forms.

Language

English (en)

Chair and Committee

Matt Kerr

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