# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics
**Dr. Bernhard
Moser**, Software Competence Center Hagenberg,
will give a public talk (followed by a discussion) on **Wed, Oct. 28, 2015**
at **16:15 o'clock** at **HS 13**
on the topic of
"Novel Research Perspectives of Weyl‘s Discrepancy Norm in Discrete Mathematics, Image and Signal Processing"
. The organziers of the symposium,

Univ.-Prof. Dr. Gerhard Larcher

A.Univ.-Prof. Dr. Jürgen Maaß, and

die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

### Novel Research Perspectives of Weyl‘s Discrepancy Norm in Discrete Mathematics, Image and Signal Processing

This presentation provides an overview of novel findings and applications of Hermann Weyl’s concept of discrepancy which constitutes a metric for probability measures. Though the concept of discprepancy is almost 100 years old, we motivate novel research perspectives of looking at this metric from the point of view of matching signals, particularly, matching images and event-based signals (spike trains) that result, e.g., from level-crossing sampling in neuromorphic systems. While the problem of monotonicity and Lipschitz continuity in image registration marks the starting point of this research, recently, the metric stability problem for event-based sampling such as integrate-and-fire has turned out to be intrinsically linked to Weyl’s discrepancy norm. This motivation from 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 as a by-product of the random walk research.