His research interests focus on the physics of systems out of equilibrium.
In order to understand these complex systems he has introduced and solved simple mathematical models, which have had multidisciplinary application, from modelling RNA translation to vehicular traffic. After postdoctoral research at Ecole Normale Superieure, Paris and the University of Oxford, Martin joined the University of Edinburgh in 1995 as a Royal Society University Research Fellow. He has served as Director of Graduate School and Director of Research of the School of Physics and Astronomy, and as Editor-in-Chief of Journal of Physics A: Mathematical and Theoretical. Over the years, he has mentored more than twenty graduate students, postdoctoral researchers and fellow academics.