Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor & Referee "Wardetzky, Max Prof. Dr."
Now showing items 1-18 of 18
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Energy-based geometric regularization in three-dimensional inverse obstacle scattering
(2024-12-13)The classic "inverse obstacle scattering problem" in three-dimensions names the challenge of reconstructing 3D-objects from (noisy) far-fied measurements of scattered waves. Like any interesting inverse problem, this ... -
Statistical Limit Laws for Graph Cuts and Efficient Surrogate Algorithms
(2024-12-05)Graph cuts are a powerful tool that has been used in many applications, from image segmentation and machine learning to network analysis and cluster identification, often in the form of a convex relaxation such as spectral ... -
A Wasserstein-like Distance on Vector Fields
(2023-10-06)We introduce a new distance on the space of vector fields over a Riemannian manifold that is motivated by the construction and properties of the Wasserstein distance. The construction relies on a particular metric on the ... -
Investigations in Hadamard spaces
(2021-08-27)This thesis investigates the interplay between geometry and convex analysis in Hadamard spaces. Motivated by numerous applications of CAT(0) geometry, our work builds upon the results in convex analysis and Alexandrov ... -
Bending energy regularization on shape spaces: a class of iterative methods on manifolds and applications to inverse obstacle problems
(2019-12-13)In applications such as nondestructive testing, geophysical exploration or medical imaging one often aims to reconstruct the boundary curve of a smooth bounded domain from indirect measurements. As a typical example we ... -
Generalized Seiberg-Witten and the Nahm Transform
(2019-01-11)Using the viewpoint of principal bundles on hyperk¨ ahler reductions, we recover the results of Gocho and Nakajima [GN92] and give insights into the role that the quater- nions play. We define a framework for dimensional ... -
New topological and index theoretical methods to study the geometry of manifolds
(2018-07-31)For a $\mathit{Spin}$ manifold $M$ the Rosenberg index $\alpha([M])$ is an obstruction against positive scalar curvature metrics. When $M$ is non-$\mathit{Spin}$ but $\mathit{Spin}^c$, Bolotov and Dranishnikov suggested ... -
A theory of discrete parametrized surfaces in R^3
(2018-07-27)In discrete differential geometry (DDG) one considers objects from discrete geometry from a differential geometric perspective. Rather than focusing on approximations of the smooth theory, with error vanishing in the ... -
Origami Cylinders
(2018-05-02)Origami, the age-old art of folding intricate three-dimensional structures from flat material, has found numerous applications in e.g. the design of deployable structures and mechanical metamaterials. This thesis ... -
Variational Estimators in Statistical Multiscale Analysis
(2016-05-24)In recent years, a novel type of multiscale variational statistical approaches, based on so-called multiscale statistics, have received increasing popularity in various applications, such as signal recovery, imaging and ... -
Variational Convergence and Discrete Minimal Surfaces
(2015-11-05)This work is concerned with the convergence behavior of the solutions to parametric variational problems. An emphasis is put on sequences of variational problems that arise as discretizations of either infinite-dimensional ... -
Projection Methods in Sparse and Low Rank Feasibility
(2015-07-07)In this thesis, we give an analysis of fixed point algorithms involving projections onto closed, not necessarily convex, subsets of finite dimensional vector spaces. These methods are used in applications such as imaging ... -
Analytic singularities near radial points
(2015-03-11)In this thesis, we applied tools of algebraic analysis and knowledge of symplectic geometry and contact geometry to give a normal form of certain class of microdifferential operators, and then studied analytic singularities of ... -
Conformal Properties of Generalized Dirac Operator
(2013-07-24)In this thesis we study the non-linear Dirac operator in dimension four and the associated generalization of the Seiberg-Witten equations in dimension four. The central object of this generalization is a hyperK ahler ... -
A discrete geometric view on shear-deformable shell models
(2012-08-15)This thesis presents the construction of a geometrically nonlinear shear-deformable (Cosserat type) shell model by methods from discrete differential geometry (DDG). The model aims at applications in real-time simulations ... -
Membrane locking in discrete shell theories
(2012-05-23)This work is concerned with the study of thin structures in Computational Mechanics. This field is particularly interesting, since together with traditional finite elements methods (FEM), the last years have seen the ... -
Persistence in discrete Morse theory
(2011-07-15)The goal of this thesis is to bring together two different theories about critical points of a scalar function and their relation to topology: Discrete Morse theory and Persistent homology. ... -
Julia Set as a Martin Boundary
(2010-11-18)The Julia set of the class of hyperbolic rational maps having a totally disconnected Julia set is here identified as the Martin boundary of a Markov chain by using symbolic dynamics. When ...