Graph theory. Twistor theory. The history of geometry.
Stephen is the General Secretary of the London Mathematical Society, and hence a Trustee of the Society. The LMS helps to inform UK research and education policy in mathematics. For the ten years to November 2011 he chaired the LMS committees responsible for awarding research grants at a scale of a third of a million pounds per year, and for formulating the UK policy input to the International Mathematical Union such as for its meeting in India in August 2010. From 2007 to 2014 Stephen was also the Secretary of the European Mathematical Society, which coordinates the work of the mathematical community in Europe, and influences European research policy.