Lie theory, Representation theory
Ion's main research area is Lie theory/representation theory. Most recently, he has been interested in Macdonald theory, which provides an uniform framework for the study of several questions regarding the spherical harmonic analysis of real/p-adic reductive groups. His work in this area makes use of various connections with affine Kac-Moody groups, Hecke algebras, the geometry of the affine Grassmannians and the affine flag manifolds, combinatorics of Coxeter groups and root systems, symmetric functions, and hypergeometric functions.
Another subject Ion works on, still deeply intertwined with the above topics but of considerable independent interest, is the representation theory of double affine Hecke algebras.