Fakultät für Mathematik und Informatik (inkl. GAUSS)
Recent Submissions

Controlling Data Streams of IoT Devices in Smart Homes from a User Perspective
(20240416)Increasingly, humans are surrounded by intelligent devices, such as smart devices, in the Internet of Things (IoT) context. These smart devices are used in various environments, such as smart environments as well as homes. ... 
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 ... 
Invariants of Kähler manifolds and Generalized SeibergWitten Equations
(20240306)The thesis explores the generalized SeibergWitten equations, a gauge theoretic differential equation arising in physics by coupling a nonlinear spinor to a connection. The study involves an analysis of the solution space ... 
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. ... 
Elliptic curves, modular forms, and the associated exponential sums
(20240227)This thesis focuses on the various arithmetic aspects of elliptic curves and modular forms. Employing the exponential sum estimates obtained from sumproduct estimates for finite fields, we estimate exponential sums linked ... 
Narrative Echoes across Time and Space
(20240216)Originating in mythological research, the Hylistic theory introduces hylemes as a basic plot unit, containing actions, states, or background information derived from a source. These statements are organized in hyleme ... 
Matching Patterns with Variables in Approximate Settings
(20240212)In the literature dealing with patterns with variables, a word, also called string, is a sequence of terminal letters, while a pattern is a sequence of terminal and variable letters. The problem of deciding if there is a ... 
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 ... 
Toward Trustworthiness of Deep Learning Models for 12Lead ECGs
(20240131)A 12lead electrocardiogram (ECG), a common examination tool in cardiology, represents the electrical activity of the heart as waveforms. Predictions and classifications with deep learning (DL) algorithms show great potential ... 
A MultiLayered Identity and Access Management Solution for Establishment of Scalable Federated Identity
(20231222)Federated identity management (FIM) systems are defined as a group of organizations (entities) that have agreed to establish trust relationships and share identity information to enable seamless access to resources across ... 
Adaptive numerical methods for optimal and branched transport problems
(20231120)Optimal transport is an area of mathematical research that has been gaining popularity in recent years in various application fields such as economics, statistics or machine learning. Two important factors behind its ... 
Improving the analysis of aeroacoustic measurements through machine learning
(20231120)This thesis focuses on improving the analysis of aeroacoustic imaging methods using automated data processing and machine learning. Imaging methods result in beamforming maps that are challenging to explore manually since ... 
Diophantine problems: inequalities and abelian varieties
(20231110)In this thesis we consider the density of rational points near manifolds and a bound for the torsion on a simple abelian variety of type IV over a number field. In the first part the main result is an asymptotic for the ... 
ServiceDifferentiated Cooperative Routing in the Internet of Things
(20231106)The IPv6 Routing Protocol for Lowpower and Lossy Networks (RPL) was designed to operate with different Internet of Things (IoT) applications ranging from regular, to critical, to alarm/sporadic. That is due to its ability ... 
Cyclotomic Norm Diophantine Equations
(20231025)In this thesis, I consider two Diophantine norm equations. For the equation of the NagellLjunggren equation $\frac{x^p1}{x1} = p^e y^q$ with distinct odd prime exponents $p, q$, I show that, for $p > 3$, it has no ... 
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 ... 
Rational points and lines on cubic hypersurfaces
(20231002)We study the solubility of cubic diophantine equations. In the first chapter, we discuss the convergence of the singular series of a cubic form, which is a central object in the study of the solutions of the associated ... 
Mathematics of Biomolecular Structure Experiments
(20230929)One of the main objectives of structural biology is to understand the complicated threedimensional structure of biomolecules, and thus provide meaningful links between structure and functionality. There is a wide range ... 
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 ... 
Weakly Regular Hyperbolic Boundary Value Problems of Real Type
(20230911)In this thesis, we derive energy estimates for weakly regular hyperbolic boundary value problems of real type, for which the Lopatinskii condition degenerates in a specific way in the socalled hyperbolic region. Such ...