Theses and Dissertations at Montana State University (MSU)
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Item Additivity of factorization algebras & the cohomology of real Grassmannians(Montana State University - Bozeman, College of Letters & Science, 2021) Berry, Eric Daniel; Chairperson, Graduate Committee: David Ayala; Ryan Grady (co-chair)This 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.Item Numerical analysis of bubble nucleation processes for first-order phase transitions within quantum fields(Montana State University - Bozeman, College of Letters & Science, 1991) Samuel, David AdrianItem Applications of quantum field theory in curved spacetimes(Montana State University - Bozeman, College of Letters & Science, 2007) Calderon, Hector Hugo; Chairperson, Graduate Committee: William A. Hiscock; Neil Cornish (co-chair)While there is as yet no full theory of Quantum Gravity, some computations can still be performed in the regime where both gravitational and quantum effects are appreciable. These types of calculations, all of them perturbations, are performed in the hope they would provide guidance for the development of the full theory. This dissertation presents work related to three calculations using Quantum Field Theory in Curved Spacetimes. Primarily, the stress energy tensor of vacuum states is computed near Big Rip singularities, sudden singularities and in presence of a Schwarzschild-(anti) de Sitter black hole. Big Rip and sudden singularities are examples of future singularities that have been attracting interest because of their relation to the latest measurements that detected accelerated expansion of the universe. A Schwarzschild-de Sitter black hole is the ultimate compact object that forms in the presence of a cosmological constant. This dissertation also contains a theorem linking the appearance of sudden singularities with the type of fluid that would drive them.