My general area of interest is complex analytic geometry. The work I have done until now lies at the interface of several complex variables, partial differential equations, and complex algebraic geometry. I find the interplay between positivity and the construction of geometric objects on the manifold to be deeply interesting. In particular, I have been studying the construction of metrics for line and vector bundles with positive curvature, and the consequences of the existence of such metrics.
In my first paper I proved the existence of a class of nontrivial solutions of the Liouville equation in even dimension.