Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Rigid Analytic Quantum Groups
(2019-04-27)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
(2019-06-01)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
(2019-03-23)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 1-5 ... -
Finite Metric Subsets of Banach Spaces
(2019-01-31)The central idea in this thesis is the introduction of a new isometric invariant of a Banach space. This is Property AI-I. A Banach space has Property AI-I if whenever a finite metric space almost-isometrically embeds into ...
