Research interests

I am interested in many different topics but, at the moment, the two most important ones include research related to

• the mathematical investigation of concept formation in language. In particular, I would like to find out if one could use the mathematical theory of topoi to generalize the idea that word meanings or, more precisely, the mathematical idea of their Gestalt, can be represented by generative structures. This is also related to recognition of meaning in data.

• the geometric Jet bundle and Diffiety approach to partial differential equations. I am particularly interested in synthetic generalizations and general approaches to the theory of PDEs. I would like to apply the results of such research to problems in Physics.

Those topics are connected by their methods since topoi (which are themselves part of category theory) are needed for a synthetic approach to differential geometry. Furthermore, they both share the characteristic that they are methodologically abstract and foundational but have powerful applications.