Theses  Pure Mathematics and Mathematical Statistics
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Rigid Analytic Quantum Groups
(20190427)Following constructions in rigid analytic geometry, we introduce a theory of $p$adic analytic quantum groups. We first define Fréchet completions $\wideparen{U_q(\mathfrak{g})}$ and $\wideparen{\mathcal{O}_q(G)}$ of the ... 
Tropical Intersection Theory on Moduli Stack of Curve Coverings
(20190601)We construct the moduli cone stack $\mathfrac{M}_\eta^\text{trop}$ of tropical \'{e}tale covers (i.e., coverings of twisted tropical curves). We define the tropical intersection theory on $\mathfrac{M}_\eta^\text{trop}$ ... 
Structure of Singular Sets Local to Cylindrical Singularities for Stationary Harmonic Maps and Mean Curvature Flows
(20190323)In this paper we prove structure results for the singular sets of stationary harmonic maps and mean curvature flows local to particular singularities. The original work is contained in Chapter 5 and Chapter 8. Chapters 15 ... 
Finite Metric Subsets of Banach Spaces
(20190131)The central idea in this thesis is the introduction of a new isometric invariant of a Banach space. This is Property AII. A Banach space has Property AII if whenever a finite metric space almostisometrically embeds into ...