Professor Francis is Director of the Centre for Research in Mathematics at Western Sydney University. His training was in Pure Mathematics at the Universities of Sydney and New South Wales, where he worked on problems in algebra related to finite reflection groups. He continued that line of research with a postdoctoral position at the University of Virginia, USA, before joining Western Sydney University in 2000.
His current research focuses a wide range of problems, mostly in biology, that require mathematical approaches from algebra, combinatorics, and graph theory. In particular, he has active interests in modelling the evolutionary processes in bacterial genomes, infectious disease transmission and evolution, in the theory of phylogenetics and phylogenetic networks, and in algebraic statistics. This work has been funded by several ARC Discovery Projects, as well as an ARC Future Fellowship 2010-2014.
He currently serves on the Australian Research Council's College of Experts, and has had active roles on the ERA Research Evaluation Committee panels. He is a Fellow of the Australian Mathematical Society.