Research InterestsMy background is in Mathematical Gauge Theory but I lean much more towards the algebro-geometric side. I study moduli of algebraic bundles and sheaves and more recently, applications of "Abstract Algebraic Geometry" to moduli problems. I was one of the founders of Fourier-Mukai Transform Theory following Mukai's ground breaking papers and now work on the interface with Bridgeland stability conditions.
I also have an interest in Mathematical Education and especially applications of AIED.
Current and Recent PhD Students
Graham Manuell (Foundations) Trang Nguyen (Algebraic Geometry) Ciaran Meachan (Algebraic Geometry, completed 2012), Dulip Piyaratne (Algebraic Geometry, completed 2013), Wafa Alagal (Algebraic Geometry, completed 2015), Manolis Mavrikis (AIED, completed 2008).
I am an Italian-Scot born in Scotland and married to Penny Morris with two daughters: Olivia and Sophie. My academic career includes degrees from Oxford and Cambridge and research fellowships held in Edinburgh. My PhD supervisor was Professor Sir Simon Donaldson and was in the subject of Gauge Theory. But I have always had a strong interest in Algebraic Geometry and especially its abstract aspects. I also have a keen interest in Mathematical Education having been involved with a number of SHEFC funded projects in collaborative teaching in Scotland. I also have an interest in various aspects of the Foundations of Mathematics.