1. Area of research
I'm interested in complex differential geometry, in particular the existence of extremal metrics on Kahler manifolds. Extremal metrics were introduced by Calabi in the 80s, and they are minimizers of various curvature functionals on Kahler manifolds. In the past 10-15 years much progress has been made in relating the existence of such metrics to algebro-geometric properties of the underlying complex manifold. I work on both the algebraic aspects related to geometric invariant theory, and the analytic questions that arise when trying to solve the relevant partial differential equation.
2. Keywords