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 ...

The purpose of this thesis is to study the (co-)homological properties of the classifying space of subsurface bundles in a trivial background bundle with fiber a manifold M. We will investigate homological stability ...

In dieser Arbeit beschäftigen wir uns mit der Modellierung und Existenztheorie von dünnen Filmen inkompressibler, viskoser Flüssigkeiten auf evolvierenden, d.h. sich bewegenden, gekrümmten Flächen. Dünne Filme treten in ...

In this thesis we consider the global routing problem, which arises as one of the major subproblems in the physical design step in VLSI design. In global routing, we are given a three-dimensional grid graph G with edge ...

We construct two functors P^strict_∂:Top →Top and ℙ^strict_∂:Top → Spectra such that for a compact manifold M the space P

The concertina is a magnetization pattern observed in elongated thin-film elements of a soft-magnetic material during the switching-process by an external magnetic field. The almost periodic pattern consists of stripe-like ...

We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions ......

We study general mechanisms that lead to aging behavior of dynamics in random environments. Aging is observed in the behavior of correlation functions that never become independent of the age of the system. A universal ...

Cancer is a major burden of disease around the globe and one of the leading causes of premature death. The key to improve patient outcomes in modern clinical cancer research is to gain insights into dynamics underlying ...

The kinetic equation describing the interaction of matter with electromagnetic waves is the radiative transfer equation. This thesis has as aim the development of a comprehensive mathematical theory for this equation. In ...