Abstract
The unifying theme of this dissertation is normal functions. In the first chapter, we study an invariant of knot exteriors and similar manifolds called the A-polynomial through the lens of vanishing loci of normal functions. Using a special case of the Zilber-Pink conjecture, proven in the second chapter, we show that only finitely many irreducible Laurent polynomials of bounded overgenus appear as factors of A-polynomials. In the third chapter, we construct normal functions from hypergeometric variations of Hodge structure and compute their regulators. Finally, we determine under which conditions incomplete motivic cohomology cycles on families complete to cycles on their Hadamard product.
Committee Chair
Matt Kerr
Committee Members
Ali Daemi; Martha Precup; N. Mohan Kumar; Roya Beheshti Zavareh; Vasily Golyshev
Degree
Doctor of Philosophy (PhD)
Author's Department
Mathematics
Document Type
Dissertation
Date of Award
4-28-2026
Language
English (en)
DOI
https://doi.org/10.7936/3qn4-je67
Author's ORCID
https://orcid.org/0000-0002-4526-0725
Recommended Citation
Akman, Devin, "Finiteness of Torsion Loci and Normal Functions Arising From Cycles on Hadamard Products" (2026). Arts & Sciences Graduate Student Theses and Dissertations. 3732.
The definitive version is available at https://doi.org/10.7936/3qn4-je67