My scientific interests include topics from different fields: information science, spatial information science, mathematics, physics, data visualization, cognitive science, and philosophy of science. This plurality has highly influenced my way of thinking and allows me to carry over methods between different fields of science. I am interested in finding answers to the following questions:
Which properties have space and time, and how do they impact spatial information?
Space and time have a simple and uniform physical structure, amongst others influencing spatial information. How can we detect such a structure in spatial information? How can we model spatial information?
Which structural properties do maps expose?
Representations differ in many structural aspects: Which aspects of information can be represented inherently? Which assumptions are implicitly assumed for a representation? etc. By understanding structural properties of maps, and contrasting it with properties of other types of representations, we can understand how certain types of information, for example spatial information, can be represented.
How can visualizations of spatial and temporal data be improved by exploiting the data's structure?
A good understanding of the data's structure and the structural opportunities offered by representations, in particular visualizations, can be used to improve the representation and to flexibly adapt it to the represented data. How can, for example, public transport networks dynamically and task-dependendly be generalized, by using structural properties of the networks and the tasks?
How can we formalize social and physical processes simultaneously in space and time?
Space and time affect us in many ways resulting in a multitude of concepts. As social processes intermesh with physical ones, concepts have to be compatible in order to formalize such processes. Yet, many concepts are, at least in parts, incommensurable. How can we gain formalizations that describe many aspects appropriately?
How can we find universal laws for spatial information?
Tobler's first law of geography is one of very few examples of universal laws that we know of in spatial science. Which additional laws exist, and how do they reflect the statistical nature of the data? Which concepts and theories in mathematics and physics can be reused in spatial information science?
How can we handle the advancing amount and the increasing heterogeneity of information?
Big data, i.e. extensive and highly heterogenous data, confronts us with many questions: How can we represent such information? How can we process data of this complexity? How can we develop suitable algorithms based on the properties of space and time? How can we visualize big data?
How can we model spatial information using mathematical and physical concepts?
Theories discussing structures (i.e. relations between entities) rather than the entities itself have turned out to be more stable under the evolutionary process of building and modifying theories, as is discussed in structural realism. Category theory and other formal approaches have contributed to the success of mathematics and physics, because they describe strong structures. Spatial information is, in many cases, affected by uncertainty and exposes only weak structures. How can we nevertheless use formal approaches to describe spatial information?
My toolbox to tackle these questions includes algebra, category theory, networks and graphs, data science, spatial reasoning, ontologies, linked (open) data technologies, information visualisation, and many more.