My interests naturally fluctuate according to all kinds of influences and state of the mind. Generally I have had long periods of interest in
modern geometry, especially but not limited to noncommutative algebraic geometry, especially applications of noncommmutative localization and Hopf algebras
sheaf theory and generalizations (including higher stacks)
mathematical physics
topology, mainly algebraic topology (and its abstract counterparts)
category theory (and more recently higher category theory)
some parts of algebra, especially homological algebra and Hopf algebras
natural and formal languages – historical linguistics, computational linguistics, programming language design, compiler optimization, semantics
See also my link-page with links to some standard online resources I use in my work.