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

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 ... 
Scalable and Reliable Framework to Detect and Mitigate DDoS Attack in OpenFlowbased SDN Network
(20230810)Softwaredefined networking in recent years has come into the sight of so many network designers as a successor to traditional networking. Unlike traditional networks where control and data planes engage together within a ... 
A Central Limit Theorem for Functions on Weighted Sparse Inhomogeneous Random Graphs
(20230713)We prove a central limit theorem for a certain class of functions on weighted sparse inhomogeneous random graphs. The proof uses a perturbative form of Stein's method and relies on a careful analysis of the local structure ... 
Aspectbased Document Similarity for Literature Recommender Systems
(20230620)Literature recommendation systems assist readers in the discovery of relevant documents. Contentbased systems recommend documents similar to the currently viewed document. However, the simple distinction between similar ... 
Propagation of polarization sets for systems of generalized transverse type and for systems of MHD type
(20230616)Polarization sets were introduced by Dencker (1982) as a refinement of wavefront sets to the vectorvalued case. He also clarified the propagation of polarization sets when the characteristic variety of the pseudodifferential ... 
Surface waves as Fourier integral operators with complex phase
(20230616)This thesis studies linear hyperbolic boundary value problems that admit surface waves as solutions. Surface waves are related to a specific type of weakly regular hyperbolic boundary value problems, where the precise ... 
Learningbased Biomimetic Strategies for Developing Control Schemes for Lower Extremity Rehabilitation Robotic Devices
(20230616)Lower limb disabilities caused by factors such as amputation, neuromuscular impairment, and traumatic injury can significantly impact mobility and quality of life. To restore impaired functionality, individuals may use ... 
Diophantine problems over global fields and a conjecture of Artin over function fields
(20230526)This thesis considers three diophantine problems over different global fields and Artin's primitive root conjecture over function fields. In the first chapter, which is a joint project with Christian Bernert, the main ... 
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 ... 
Interpreting and visualizing the decisions of Deep Neural Networks
(20230420)Machine learning and its associated algorithms involving deep neural networks have gained widespread admiration in the computer vision domain. In this regard, significant progress has been made in automating certain ... 
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 ... 
Highorder Unfitted Discretizations for Partial Differential Equations Coupled with Geometric Flow
(20230217)We consider a moving free boundary problem where a diffusion equation posed on an evolving domain bounded by a smooth surface is coupled with a mean curvature flow of the bounding surface. The evolution velocity of the ... 
Aperiodic dynamical inclusions of C*algebras
(20230216)We define an analogue of the local multiplier algebra for Hilbert modules and use properties of this localisation to enrich nonclosed actions on C*algebras to closed actions on local multiplier algebras. This is used to ... 
Mineralogical mapping of selected areas of the lunar surface using Moon Mineralogy Mapper data.
(20230112)The dissertation is concerned with spectrophotometric studies of selected areas of the lunar surface using the data generated by the mapping spectrometer Moon Mineralogy Mapper (M3), onboard the Chandrayaan1 spacecraft. ... 
Phylogenetic Forest Spaces
(20230110)Given a fixed set of operational taxonomic units (OTUs), when studying their evolutionary relationships among each other, a common way of depicting those is to construct a phylogenetic tree, a graphtheoretic tree with a ... 
GromovWasserstein Distances and their Lower Bounds
(20221125)In various applications in biochemistry, computer vision and machine learning, it is of great interest to compare general objects in a pose invariant manner. Recently, the following approach has received increased attention: ... 
Über J. Bernsteins zweite Adjungiertheit für reduktive padische Gruppen
(20221025)We give a new and essentially elementary proof of an important result due to Joseph Bernstein in the theory of smooth representations of a reductive padic group G. Main tools for studying these representations are parabolic ...