Young, BenjaminWebb, Gautam2021-11-232021-11-232021-11-23https://hdl.handle.net/1794/26871We resolve an open conjecture from algebraic geometry, which states that two generating functions for plane partition-like objects (the "box-counting" formulae for the Calabi-Yau topological vertices in Donaldson-Thomas theory and Pandharipande-Thomas theory) are equal up to a factor of MacMahon's generating function for plane partitions. The main tools in our proof are a Desnanot-Jacobi-type condensation identity, and a novel application of the tripartite double-dimer model of Kenyon-Wilson.en-USAll Rights Reserved.Desnanot-Jacobi identityDonaldson-Thomas theorydouble-dimer modelPandharipande-Thomas theoryplane partitionsElectronic Thesis or Dissertation