My Research Interests

My research interests are broad; I am mainly interested in structures that unify different areas of mathematics and mathematical physics. I am particularly interested in category theory, for its internal beauty as well as for its power to unify traditional concepts of topology, functional analysis, etc... .

In this spirit, I have been working on Banach modules and operator modules.

Presently, I am working on a rigorous and useful definition of higher dimensional categories. It is closely modeled on the omega-category associated to a topological space. In this example the n-morphisms are continuous maps from the n-dimensional cube to the topological space.