# Fundamental mathematics

University of Antwerp research units working in the fundamental mathematics areas of algebra, geometry and topology have long been recognised both in Flanders and internationally as centres for excellence in research in fundamental structural mathematics.

This research area concentrates on the fields of noncommutative algebraic geometry and categorical topology. As far as the algebraic-geometric aspect is concerned, this means studying sheaves, localisations, graded and filtered rings, projective spaces, derived algebraic geometry, homological and homotopical algebra, deformation and Hochschild cohomology, deformation quantisation and Hopf algebra. The analytical-topological aspect, on the other hand, is concerned with topological categories, topological spaces, "approach" theory, metrically generated theories, linear algebraic theories, point-free topology and "frames", Clifford analysis and invariant operators.

These theories have their roots in a multitude of often very varied inherently mathematical problems from both directly and indirectly related mathematical fields, including approximation theory, measure and probability theory, and functional and complex analysis. Theories stemming from geometric algebra and Clifford analysis, in particular, also have several applications in theoretical physics.