Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor & Referee "Schick, Thomas Prof. Dr."
Now showing items 1-20 of 60
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Classifying spaces for quasi-topological groups
(2025-10-24)This thesis provides a quick introduction into quasi-topological spaces, first introduced by Spanier. It then constructs notions of numerable principal G-bundles in the quasi-topological case and constructs a quasi-topological ... -
The Minimal Hypersurface Method to Obstruct Positive Scalar Curvature via the Classification of 3-Manifolds
(2025-05-05)In 1979, Schoen and Yau developed a method using descending chains of minimal hypersurfaces to obstruct psc for manifolds initially up to dimension 7. Recent results on regularity for minimal hypersurfaces extend the ... -
C*-algebras of relatively proper groupoid correspondences
(2024-12-09)The objective of the work is to study C*-algebras associated to relatively proper groupoid correspondences, in particular exploring two constructions and proving that they are isomorphic. We also explore some properties ... -
Generalizations of Quandles to Multi-Linkoids
(2024-04-10)In this thesis, we define the fundamental quandle of knotoids and linkoids and prove that it is invariant under the under forbidden-move and hence encodes only the information of the underclosure of the knotoid. We ... -
The Spectra on Lie Groups and Its Application to twisted L2-Invariants
(2024-02-29)We computed spectra of various $G$-invariant differential operators on the universal cover of 2x2 unimodular groups. This was achieved by applying tools from harmonic analysis/representation theory to corresponding groups. ... -
An Integration Theorem for Representations of the Tangent Algebroid
(2024-02-09)This dissertation investigates representations of Lie groupoids and Lie algebroids and the connection between them. Lie groupoids and Lie algebroids are differential-geometric generalisations of Lie groups and Lie ... -
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 ... -
Twisted equivariant K-theory and equivariant T-duality
(2023-09-18)This thesis is about two things: twisted equivariant K-theory and equivariant topological T-duality. First, we prove a fixed point decomposition theorem for twisted equivariant K-theory, generalising a result of Atiyah and ... -
Novikov-Shubin Invariants of Nilpotent Lie Groups
(2023-05-25)Novikov-Shubin invariants are so-called L2-invariants of non-compact manifolds. They are defined using the Laplace operators and measure the density of their spectra near zero. This near-zero part of the spectrum is ... -
Concordances in Positive Scalar Curvature and Index Theory
(2023-02-24)We apply the strategy to study of diffeomorphisms via block diffeomorphisms to the world of positive scalar curvature (psc) metrics. For each closed psc manifold, we construct the cubical set of all psc block metrics, the ... -
Aperiodic dynamical inclusions of C*-algebras
(2023-02-16)We define an analogue of the local multiplier algebra for Hilbert modules and use properties of this localisation to enrich non-closed actions on C*-algebras to closed actions on local multiplier algebras. This is used to ... -
Nahms Equations and Nilpotent Orbits
(2022-05-31)P. Kronheimer has identified certain space of solutions to Nahms equations with a coadjoint orbit of a nilpotent element in a complex, semi-simple Lie algebra and that way equipped the orbit with an hyperkähler structure ... -
Foliated Positive Scalar Curvature
(2021-11-11)In this thesis we study different questions on scalar curvatures. The first part is devoted to obstructions against existence of a (Riemannian) metric with positive scalar curvature on a closed manifold. The second ... -
Lie Algebras and the Dimension Problem
(2021-11-03)The dimension subgroup problem and the Ore conjecture are two group theoretical problems. In this thesis, translations of these problems to Lie algebras are analyzed and partially solved. -
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 ... -
Continuous Wavelet Transformation on Homogeneous Spaces
(2021-03-29)The classical Continuous Wavelet Transformation (cCWT) is an important and well-studied tool in signal processing and data analysis. Because of its deep connection to representation theory, it has come into focus of pure ... -
Index theory and groupoids for filtered manifolds
(2020-12-21)In this thesis, we propose to use generalized fixed point algebras as an approach to the pseudodifferential calculus on filtered manifolds. A filtered manifold is a manifold \(M\) with a filtration of its tangent ... -
L²-Invariants for Self-Similar CW-Complexes
(2020-11-11)L²-invariants are commonly defined only for periodic spaces, that is, spaces with a cocompact action by some discrete group. This thesis develops a theory of L²-invariants for quasi-periodic spaces instead, where the group ... -
The Barban-Davenport-Halberstam for tuples of k-free numbers
(2020-10-23)An asymptotic formula for variance of tuples of k-free numbers in arithmetic progressions -
Topological Invariants for Non-Archimedean Bornological Algebras
(2020-10-13)In this thesis, we define a cyclic homology theory for non-archimedean bornological algebras, which we call analytic cyclic homology. Let V be a complete, discrete valuation ring with uniformiser p, residue field k, and ...