Prof. Dr. Hans-Peter A. Künzi

Current professional background

I am a full Professor at the Department of Mathematics and Applied Mathematics of the University of Cape Town, in Rondebosch, South Africa.

Field of research

Topology, orders, categories, combinatorics and their applications in analysis and algebra; focus on asymmetric

Purpose of your last research visit

A central concept of applied mathematics is the notion of a metric space, that is, a set of points equipped with a symmetric real-valued distance function. The motivation for such investigations originates for instance in planar geometry. If however one models surfaces with hills and valleys and one plans to measure the distance between two points A and B by the energy needed to move from A to B, then the symmetry condition in general is no longer satisfied. This variant leads to the weaker concept of a quasi-metric. One advantage of this generalisation is that now also applications are possible in the field of computer science. In this area in particular the weighted quasi-metrics are of interest, which often appear as partial metrics.

An interesting problem is to measure the degree of symmetry of a given distance function d. In order to treat this question, it is natural to determine the distance of d to some symmetrisation of d. To this end there exist various approaches in the mathematical literature, which we have studied and compared during my stay. This led for instance to a cooperation with a research group form Hacettepe University in Ankara. Towards the end of my visit I gave a talk about generalised metrics at the conference “International Conference on Topology and its Applications” in Nafpaktos, Greece. As in a previous visit to Siegen, besides my research activities, I did in Siegen some teaching for Masters students about the theory of graphs. In this way I could also participate in several meetings of the Department of Mathematics in Siegen.

This offered me the opportunity to make comparisons between administrative work done in Siegen and in Cape Town. Furthermore I had many interesting discussions with the students and a student tutor associated with my course.

Relation to the University of Siegen and the local host

My host, Prof. Dr. Spreen, in Siegen and I have known each other for many years and always appreciate our joint scientific discussions. We had many opportunities for such discussions during my recent visit, as in the past during our regular visits to Cape Town (Siegen, respectively). For instance I had already spent several months of my sabbatical of 2011 at the University of Siegen.

Future projects and Activities

It is planned that the existing fruitful collaboration between the Universities of Cape Town and Siegen will be continued. During my stay in Siegen Prof. Dr. Spreen and I discussed how the funding of future exchange visits could be secured in the years to come.

Impressions of Siegen

After my usual work in Cape Town, I always like to return to the town of Siegen, since over the years I have always found it to be a relatively quiet place, which has clearly furthered my mathematical research.