Chairperson, Graduate Committee: David Ayala; Ryan Grady (co-chair)Berry, Eric Daniel2022-01-252022-01-252021https://scholarworks.montana.edu/handle/1/16314This dissertation is composed of two separate projects. The first chapter proves two additivity results for factorization algebras. These provide a way to understand factorization algebras on the product of two spaces. Our results can be thought of as a generalization of Dunn's additivity for En-algebras. In particular, our methods provide a new proof of Dunn's additivity. The second chapter is an examination of the Schubert stratification of real Grassmann manifolds. We use this extra structure to identify the quasi-isomorphism type of the Schubert CW chain complex for real Grassmannians. We provide explicit computations using our methods.enGeometry, DifferentialAlgebraic topologyHomology theoryQuantum field theoryDissertationCopyright 2021 by Eric Daniel Berry