Afandi, Adam, authorCavalieri, Renzo, advisorShoemaker, Mark, advisorAdams, Henry, committee memberPrasad, Ashok, committee member2021-06-072021-06-072021https://hdl.handle.net/10217/232591This dissertation explores the combinatorial structures that underlie hyperelliptic Hodge integrals. In order to compute hyperelliptic Hodge integrals, we use Atiyah-Bott (torus) localization on a stack of stable maps to [P1/Z2] = P1 × BZ2. The dissertation culminates in two results: a closed-form expression for hyperelliptic Hodge integrals with one λ-class insertion, and a structure theorem (polynomiality) for Hodge integrals with an arbitrary number of λ-class insertions.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.Text