E-Dissertationen: Suche
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On some variational problems in geometry
(2018-08-28)
In this thesis we consider several variational problems in geometry that have a connection to the spectrum of the Laplacian acting on functions. In the first part, we study a quantity called the analytic systole, which was ...
On the geometry of nodal sets and nodal domains
(2018-12-13)
In the present work, we study and prove results related to the nodal geometry of Laplacian eigenfunctions on closed Riemannian manifolds, as well as solutions to more general classes of elliptic partial differential ...
Scalable Algorithms for Parallel Tree-based Adaptive Mesh Refinement with General Element Types
(2018-12-12)
In this thesis, we develop, discuss and implement algorithms for scalable parallel tree-based adaptive mesh refinement (AMR) using space-filling curves (SFCs). We create an AMR software that works independently of the used ...
G-theory of group rings for finite groups
(2018-12-13)
In this thesis we investigate Quillen's G-theory of group rings mostly focusing on the case of finite groups. We study the Hambleton-Taylor-Williams decomposition conjecture for G-theory of the integral group rings. The ...
On discrete surfaces: Enumerative geometry, matrix models and universality classes via topological recursion
(2019-03-21)
The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. We approach our study of these objects from different perspectives, namely bijective combinatorics, matrix ...
Scalable parallel simulation of variably saturated flow
(2019-03-19)
In this thesis we develop highly accurate simulation tools for variably saturated flow through porous media able to take advantage of the latest supercomputing resources. Hence, we aim for parallel scalability to very large ...
Assembly Maps and Pseudoisotopy Functors
(2019-05-03)
In this thesis we show the existence of a stable, smooth pseudoisotopyfunctor and construct in the topological, piecewise linear, and smooth category a zig-zag of natural weak equivalences between the stable pseudoisotopyfunctor ...
Uniform estimates in one- and two-dimensional time-frequency analysis
(2019-02-22)
This thesis is concerned with two special cases of the singular Brascamp-Lieb inequality, namely, the trilinear forms corresponding to the one- and two-dimensional bilinear Hilbert transform. In this work we study the ...
On the effective properties of suspensions
(2019-02-04)
Einstein's formula for the viscosity of dilute suspensions describes how rigid particles immersed in a Stokes-fluid increase its macroscopic viscosity in terms of the particle volume density ∅. However, up to now, a rigorous ......
Sparse representation of multivariate functions based on discrete point evaluations
(2019-01-22)
Functions provide one of the most important building blocks for model descriptions of reality. Central point of this thesis is the approximation of multivariate functions using Faber-Schauder hat functions. In the first ...