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 ...

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 ...

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 ...

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

Placement is an important step in the process of finding physical layouts for electronic computer chips. The basic task during placement is to arrange the building blocks of the chip, the circuits, disjointly within a given ...

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 ...

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 ...

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 ...

Axis-aligned rectangle packings can be characterized by the set of spatial relations that hold for pairs of rectangles (west, south, east, north). A representation of a packing consists of one satisfied spatial relation ...

Cell layout is a critical step in the design process of computer chips. A cell is a logic function or storage element implemented in CMOS technology by transistors connected with wires. As each cell is used many times on ...