Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Schick, Thomas Prof. Dr."
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Generalizations of Quandles to MultiLinkoids
(20240410)In this thesis, we define the fundamental quandle of knotoids and linkoids and prove that it is invariant under the under forbiddenmove and hence encodes only the information of the underclosure of the knotoid. We ... 
The Spectra on Lie Groups and Its Application to twisted L2Invariants
(20240229)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
(20240209)This dissertation investigates representations of Lie groupoids and Lie algebroids and the connection between them. Lie groupoids and Lie algebroids are differentialgeometric generalisations of Lie groups and Lie ... 
A Wassersteinlike Distance on Vector Fields
(20231006)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 Ktheory and equivariant Tduality
(20230918)This thesis is about two things: twisted equivariant Ktheory and equivariant topological Tduality. First, we prove a fixed point decomposition theorem for twisted equivariant Ktheory, generalising a result of Atiyah and ... 
NovikovShubin Invariants of Nilpotent Lie Groups
(20230525)NovikovShubin invariants are socalled L2invariants of noncompact manifolds. They are defined using the Laplace operators and measure the density of their spectra near zero. This nearzero part of the spectrum is ... 
Concordances in Positive Scalar Curvature and Index Theory
(20230224)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 ... 
Nahms Equations and Nilpotent Orbits
(20220531)P. Kronheimer has identified certain space of solutions to Nahms equations with a coadjoint orbit of a nilpotent element in a complex, semisimple Lie algebra and that way equipped the orbit with an hyperkähler structure ... 
Foliated Positive Scalar Curvature
(20211111)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
(20211103)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
(20210827)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
(20210329)The classical Continuous Wavelet Transformation (cCWT) is an important and wellstudied 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
(20201221)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 ... 
The BarbanDavenportHalberstam for tuples of kfree numbers
(20201023)An asymptotic formula for variance of tuples of kfree numbers in arithmetic progressions 
Topological Invariants for NonArchimedean Bornological Algebras
(20201013)In this thesis, we define a cyclic homology theory for nonarchimedean bornological algebras, which we call analytic cyclic homology. Let V be a complete, discrete valuation ring with uniformiser p, residue field k, and ... 
Index Theory and Positive Scalar Curvature
(20200724)The aim of this dissertation is to use relative higher index theory to study questions of existence and classification of positive scalar curvature metrics on manifolds with boundary. First we prove a theorem relating ... 
BenjaminiSchramm Convergence of Normalized Characteristic Numbers of Riemannian Manifolds
(20200430)We study a weak form of GromovHausdorff convergence of Riemannian manifolds, also known as BenjaminiSchramm convergence. This concept is also applicable to other areas and has widely been studied in the context of ... 
A MayerVietoris Spectral Sequence for C*Algebras and Coarse Geometry
(20190410)Let $A$ be a C*algebra that is the norm closure $A = \overline{\sum_{\beta \in \alpha} I_\beta}$ of an arbitrary sum of C*ideals $I_\beta \subseteq A$. We construct a homological spectral sequence that takes as input the ... 
Generalized SeibergWitten and the Nahm Transform
(20190111)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 ... 
Shape space in terms of Wasserstein geometry and application to quantum physics
(20181126)This thesis offers a mathematical framework to treat quantum dynamics without reference to a background structure, but rather by means of the change of the shape of the state. For this, Wasserstein geometry is used. The ...