Peter Collins' research is in analytic topology and differential equations. Books and articles in mathematical journals, including A general compactness theorem (Proceedings of the Cambridge Philosophical Society, 1970), referred to in Encyclopaedia Britannica, Criteria for metrisability(with A.W. Roscoe, Proceedings of the American Mathematics Society, 1984), On the topological structure of curves (in The Heritage of C.F.Gauss, World Scientific Publications,1991), On submaximal spaces (with A.V. Arhangel’skii, Topology and its Applications, 1995), Monotone Normality (Topology and its Applications, 1996) and Differential and Integral Equations (OUP, 2006).

Invited lectures in more than 30 countries, including senior visiting positions in the United States, France and New Zealand.

Head of the Analytic Topology Research Group at the Mathematical Institute, and formerly Chairman of the Mathematical Sciences Faculty Board and Vice-Chairman of the General Board of the Faculties in the University.  Formerly Dean, Senior Tutor, and Investment and Senior Bursar of the College.