Within the field of mathematics, Jan van Mill carries out research into topological groups, the topology of infinite dimensional manifolds, dimension theory and set-theoretic topology. He also has an interest in the history of topology.
Knowledge of the symmetry groups of geometric objects is essential when conducting research into the structure of the latter. Due to the nature of geometric objects, their symmetry groups are complex and consist of more than simply rigid motions. For example, these groups in particular are of an infinite size. This means that not only is the algebraic structure of these groups important, but also their topological structure. Topology formalises the concept of proximity of transformations. Van Mill's work concentrates on the topological classification of such objects.
Van Mill is Emeritus Professor of Mathematics at VU University Amsterdam, to which he has been affiliated since 1974. From 2006 to 2010, Van Mill served as Dean of the Faculty of Sciences. He was affiliated with the UvA for a number of years on a part-time basis in the 1980s. Van Mill is a member of the academic committee of the Institut de Mathemàtiques i Applications de Castelló of the Universitat Jaume I (Spain) and of the committee for mathematics and statistics of the Natural Sciences and Engineering Council of Canada. Van Mill is affiliated with various academic journals, for instance as editor-in-chief of the journal 'Topology and its Applications'.