Research

My research interests are within algebraic geometry and complex algebraic geometry, and links between the two. In particular I am interested notions of stability (in the sense of Geometric invariant theory) both for sheaves and for varieties. In particular I work on the relationship between stability and Kähler geometry, via the existence of special metrics (for example Kähler-Einstein metrics or Hermitian-Einstein metrics).

I am also interested in the theory of singular hermitian metrics and some aspects of pluripotential theory as well as the inverse moment problem in the plane and solutions to the Hele-Shaw flow.

Recently I have been working on generalizations of the Hodge-Riemann bilinear relations.