Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 35 for “"Riemannian Geometry"”.
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Aspects of Riemannian geometry in quantum field theories
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1999.
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On the Riemannian geometry of Seiberg-Witten moduli spaces
In this thesis, we give two constructions for Riemannian metrics on Seiberg-Witten moduli spaces. Both these constructions are naturally induced from the L2-metric on the configuration space. The construction of the so called quotient L2-metric is very similar to the one construction of an …
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Riemannian geometry for inverse problems in cryogenic electron microscopy
This thesis develops theory and algorithms for a Riemannian geometric approach to inverse problems in cryogenic electron microscopy (Cryo-EM). It is divided into two parts, motivated by the sub problem of orientation estimation and that of modelling of protein dynamics. The thesis is concluded with …
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Towards Learning the Geometry of Data: From Diffusion Models to Riemannian Geometry
… modelling, self-supervised learning, and Riemannian geometry, paving the way for learning the intrinsic geometry of data manifolds. In chapter 3, we introduce CAFLOW, a conditional normalising flow that improves image-to-image translation by hierarchically modelling image distributions …
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Riemannian geometry of matrix manifolds for Lagrangian uncertainty quantification of stochastic fluid flows
… the mathematical foundations of the method. Riemannian geometry providing an appropriate setting, a framework free of tensor notations is used to analyze the embedded geometry of three popular matrix manifolds, namely the fixed rank manifold, the Stiefel manifold and the isospectral manifold. …
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Comparison and Development of Algorithms for Motor Imagery Classification in EEG- based Brain-Computer Interfaces
… used classification based on concepts from Riemannian geometry. The basic idea of these methods is that sample spatial covariance matrices (SCMs) of EEG epochs belong to the Riemannian manifold of symmetric positive-definite (SPD) matrices and that the tangent space at any SPD matrix on the …
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New and old sub-Riemannian challenges bridging analysis and geometry
… geometric problems arising from the study of sub-Riemannian geometry, Carnot-Carathéodory spaces and, more broadly, anisotropic metric and differential structures. We deal with four main topics. 1 Calculus of variations for local functionals depending on vector fields 2 PDEs over …
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Scalar Curvature Constraints on Symplectic 4-Manifolds
… that showcases an unexpected interplaybetween Riemannian geometry and symplectic topology on 4-manifolds. These two branches of mathematics belong to different worlds: Where geometry concerns it- self with distances, angles, areas, curvatures, etc., all of which typically vary from one point on …
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Geometry of sub-Riemannian diffusion processes
Sub-Riemannian geometry is the natural setting for studying dynamical systems, as noise often has a lower dimension than the dynamics it enters. This makes sub-Riemannian geometry an important field of study. In this thesis, we analysis some of the aspects of sub-Riemannian diffusion processes on …
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A Study of the Multiple-Unicast Network Coding Conjecture Using Riemannian Manifolds
… we study the conjecture by embedding graphs into Riemannian manifolds using a geometric framework developed by Xiahou el al. [32]. We prove that isometric embedding of graphs into a Riemannian manifold is impossible. Then, interestingly, we construct an embedding that achieves an infinitesimally …
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Traversing Rugged Domains: Explorations in Non-convex Optimization Theory and Software
… (DGCP) extends convexity verification to Riemannian manifolds, enabling optimization on curved spaces with global optimality guarantees. We develop rules and atoms for Cartan-Hadamard manifolds, particularly symmetric positive definite matrices, transforming non-convex problems into …
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The noncommutative geometry of ultrametric cantor sets
An analogue of the Riemannian structure of a manifold is created for an ultrametric Cantor set using the techniques of Noncommutative Geometry. In particular, a spectral triple is created that can recover much of the fractal geometry of the original Cantor set. It is shown that this spectral triple …
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Geometry of Spaces of Planar Quadrilaterals
… of this dissertation is to investigate the geometry of spaces of planar quadrilaterals. The topology of moduli spaces of planar quadrilaterals (the set of all distinct planar quadrilaterals with fixed side lengths) has been well-studied [5], [8], [10]. The symplectic geometry of these spaces …
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PERFECT FLUIDS AND SIGMA MODELS: A MATHEMATICAL INVESTIGATION BETWEEN GENERAL RELATIVITY AND COTTON GRAVITY
… we deal with two physics-inspired structures on Riemannian manifolds, depending on a smooth map φ between Riemannian manifolds and several other functions and constants; they are called Cotton φ-Perfect Fluids (C-φ-PF) and φ-static perfect fluids space-times (φ-SPFST). The latter are special …
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Nonlinear Methods in the Study of Singular Partial Differential Equations
… when studying models from such areas as Riemannian geometry, applied probability, mathematical physics and biology. The purpose of this thesis is to develop analytical methods to investigate a large class of nonlinear elliptic PDEs underlying models from physical and biological sciences. …
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Computational crowd camera : enabling remote-vision via sparse collective plenoptic sampling
… be regarded as the result of discretizing the Riemannian geometry of the high dimensional manifold of all possible photos. Ultimately, this system enables everyday people to take advantage of each others' perspectives in order to create on-the-spot spatiotemporal visual experiences similar to …
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Discrepancy Inequalities in Graphs and Their Applications
… but rather a different tool with motivations in Riemannian geometry.</p> <p>The first problem explored in this dissertation is motivated by parallel computing and other communication networks. Consider a connected graph <em>G</em>, with a pebble placed on each vertex of <em>G</em>. The routing …
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Attitude control on manifolds via optimization and contractions with automatic gain tuning
… generalization on the theory of classical Riemannian metrics for tangent bundles which provides the ability to compare and combine attitude and velocity terms in the stability analysis, allowing us to consider a larger set of feasible controller gains. The second contribution is a framework …
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Ambient Obstruction Solitons And Homogeneous Gradient Bach Solitons
<p>Differential geometry is a diverse field which applies principles from calculus to a more general set of objects. Endowing a smooth manifold with a Riemannian metric allows us to measure length and angle in a way such that length is positive. This enables us to examine measures of curvature on a …
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Ambient Obstruction Solitons and Homogeneous Gradient Bach Solitons
<p>Differential geometry is a diverse field which applies principles from calculus to a more general set of objects. Endowing a smooth manifold with a Riemannian metric allows us to measure length and angle in a way such that length is positive. This enables us to examine measures of curvature on a …
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