Mathematics
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Regular homomorphisms of minimal sets
(1974)The classification of minimal sets is a central theme in abstract topological dynamics. Recently this work has been strengthened and extended by consideration of homomorphisms. Background material is presented in Chapter ... 
Quantitative Derivation of Effective Evolution Equations for the Dynamics of BoseEinstein Condensates
(2016)This thesis proves certain results concerning an important question in nonequilibrium quantum statistical mechanics which is the derivation of effective evolution equations approximating the dynamics of a system of large ... 
Fundamental domains for proper affine actions of Coxeter groups in three dimensions
(2016)We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A ... 
Spectral Frame Analysis and Learning through Graph Structure
(2016)This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first ... 
Analysis of SelfOrganization
(2016)The dissertation is devoted to the study of problems in calculus of variation, free boundary problems and gradient flows with respect to the Wasserstein metric. More concretely, we consider the problem of characterizing ...