My research falls mostly under the broad theme of 'Humeanism', which I take to be the view that there is no such thing as natural necessity (or, if there is, it is a fairly superficial rather than a fundamental feature of reality).
I've written on some central aspects of the debate about Humeanism, including whether or not the laws of nature 'govern' what happens ('The non-governing conception of laws of nature', Philosophy and Phenomenological Research 56 (2000)), whether Humeanism entails inductive scepticism ('Necessary connections and the problem of induction', Nous 45 (2011)), and whether causal relations are observable ('Seeing causing', Proceedings of the Aristotelian Society 103 (2003)).
I've also written on Hume himself, including Hume on Causation (Routledge 2006) and 'Hume's two definitions' (Hume Studies 37 (2011)).
I also have an interest in freedom of the will, and in particular in defending compatibilism - e.g. in 'Humean compatibilism' (Mind 111 (2002), with Al Mele) -- which brings a Humean conception of laws to bear on van Inwagen's Consequence Argument, in response to a worry about Lewis's compatibilist account that I raise in 'Local Miracle Compatibilism' (Nous 37 (2003))-- and 'Smilansky's alleged refutation of compatibilism' (Analysis 68 (2008)).
I currently have an edited collection in press, Making a Difference, with Chris Hitchcock and Huw Price. It includes papers that engage in one way or another with the work of Peter Menzies; the contributing authors include Nancy Cartwright, Alison Gopnik, Jonathan Schaffer and Jim Woodward.