For completing the habilitation!
Research on the concept of discrepancy
Dr. Bernhard Moser's habilitation entitled Novel Research Perspectives of Weyl‘s Discrepancy Measure
in Discrete Mathematics, Image and Signal Processing.
Novel findings an applications of Hermann Weyl's concept of discrepancy which constitutes a metric for probability measures
Though 100 years old, novel research perspectives of Wey’s discrepancy come about by looking at this metric from the point of view of matching images and signals. While the problem of monotonicity and Lipschitz continuity in image registration marks the starting point of this story, recently, the stability problem of event-based sampling as encountered in neuromorphic sensory systems has turned out to be intrinsically linked to Weyl’s discrepancy. This applied research has also brought about novel pure mathematical findings in discrete geometry and combinatorics: a) the characterization of the n-dimensional unit ball of Weyl's discrepancy norm in terms of a zonotope, b) a lattice path enumeration approach for determining the distribution of the range of a simple random walk, which provides an elementary solution to a problem stated by Feller 1951, and c) novel Pascal triangle identities which are related to Fibonacci numbers.