UC San Diego

This dissertation explores three projects. In the first, we construct and analyze topological quantum error-detecting codes that encode cohomology and homology. This project concludes by using the excitations of these types of codes to encode obstruction classes of fiber bundles. This research builds into the second project, in which we introduce a new formal definition of a particular subset of topological codes and reverse-engineer a characterization of these codes. It ends with the construction of a conjectured novel topological code. Separately, the third project is in game theory. Here, we propose a novel definition of fairness and playability, then find the most unfair yet playable variant of Rock-Paper-Scissors (RPS). We conclude by extending these ideas to construct a conjectured, strongly playable, maximally unfair RPS with m players.