Combinatorial structures of hyperelliptic Hodge integrals
Date
2021
Authors
Afandi, Adam, author
Cavalieri, Renzo, advisor
Shoemaker, Mark, advisor
Adams, Henry, committee member
Prasad, Ashok, committee member
Journal Title
Journal ISSN
Volume Title
Abstract
This 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.