Frank Kelly was elected a Research Fellow of Christ's College in 1976, and served as Director of Studies in Mathematics and a Tutor. He was elected the 37th Master of the College in December 2006.

His main research interests are in random processes, networks and optimization. He works on the mathematics of very large-scale systems, such as telecommunication or transport networks. Particular interests have been dynamic routing and resource allocation in communication networks, including the Internet. He is Professor of the Mathematics of Systems in the University.

He spent the academic year 2001-2002 as a Visiting Professor at Stanford University in the USA. From 2003-2006 he served as Chief Scientific Adviser to the UK Government’s Department for Transport, and in 2011-12 as a non-executive director of Autonomy plc. He is a Trustee of RAND Europe and Chair of the Council for the Mathematical Sciences.

He was elected a Fellow of the Royal Society in 1989, and a Foreign Associate of the National Academy of Engineering in 2012.