Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor & Referee "Meyer, Ralf Prof. Dr."
Now showing items 1-20 of 35
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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 ... -
Higher Currents for the sine-Gordon Model in perturbative Algebraic Quantum Field Theory
(2024-09-19)The main results of this thesis are the establishment of the super-renormalizability by power counting and of the summability of an infinite number of (classically conserved) higher currents for the sine-Gordon model in ... -
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 ... -
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 ... -
Über J. Bernsteins zweite Adjungiertheit für reduktive p-adische Gruppen
(2022-10-25)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 p-adic group G. Main tools for studying these representations are parabolic ... -
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 ... -
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 ... -
Index Theory and Positive Scalar Curvature
(2020-07-24)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 ... -
Benjamini-Schramm Convergence of Normalized Characteristic Numbers of Riemannian Manifolds
(2020-04-30)We study a weak form of Gromov-Hausdorff convergence of Riemannian manifolds, also known as Benjamini-Schramm convergence. This concept is also applicable to other areas and has widely been studied in the context of ... -
A Mayer-Vietoris Spectral Sequence for C*-Algebras and Coarse Geometry
(2019-04-10)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 ... -
Groupoids in categories with partial covers
(2019-02-07)Meyer and Zhu survey the general theory of groupoids, groupoid actions, groupoid principal bundles, and various kinds of morphisms between groupoids in the framework of categories with pretopology. We modify the categorical ... -
Exakte Moduln über dem von Manuel Köhler beschriebenen Ring
(2018-11-13)When proving an equivariant universal coefficient theorem for C*-Algebras acted on by a finite cyclic group Z/pZ, Manuel Köhler introduces the endomorphism ring R of the tuple (C,C(G),D). The aim of this thesis is to show ... -
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 ... -
Algorithms for structured nonconvex optimization: theory and practice
(2018-07-24)We first synthesize and unify notions of regularity, both of individual functions/sets and of families of functions/sets, as they appear in the convergence theory of fixed point iterations. Several new primal and dual ... -
On C*-algebras associated to product systems
(2018-05-17)We consider a class of Fell bundles over quasi-lattice ordered groups. We show that these are completely determined by the positive fibres and that their cross sectional C*-algebras are relative Cuntz–Pimsner algebras ... -
Characters on infinite groups and rigidity
(2018-05-02)We show that for a strong extension of discrete measured groupoids $1\to\mathcal{S}\to\mathcal{G}\to\mathcal{Q}\to 1$ with $L\mathcal{G}$ a finite factor, $\mathcal{Q}$ has poperty (T) if and only if the inclusion of ... -
Coarse Geometry for Noncommutative Spaces
(2016-11-23)We develop an analogoue of coarse geometry for noncommutative spaces in terms of unitizations of the given C* -algebra. Examples for our theory come from Rieffel deformation of compactifications under strongly continuous ... -
Secondary large-scale index theory and positive scalar curvature
(2016-09-06)We develop a theory of secondary invariants associated to complete Riemannian metrics of uniformly positive scalar curvature outside a prescribed subset on a spin manifold. We work in the context of large-scale (or "coarse") ...