After completing my undergraduate degree at Cambridge in 1995, I moved to Edinburgh to study for a PhD under Antony Maciocia. My thesis `Fourier-Mukai transforms for surfaces and moduli spaces of stable sheaves' was completed in 1998. I held a series of postdoctoral positions at Edinburgh and then Sheffield, including a Royal Society University Research Fellowship. In 2012 I was elected to a Senior Research Fellowship at All Souls College, Oxford. I resigned this in 2013 to return to a position at Sheffield.

I am an algebraic geometer with a particular interest in homological methods and interactions with string theory. My main focus is on properties of derived categories of coherent sheaves on algebraic varieties. These arise in string theory as categories of D-branes, and are related via Kontsevich's famous homological mirror symmetry conjecture to Fukaya categories of symplectic manifolds. Categories with similar properties and a more explicit flavour can be defined using representations of quivers. Other closely related mathematical areas I have an interest in are Donaldson-Thomas invariants and Hall algebras.