Partial differential equations and geometric analysis
Research Statement: I am interested in problems in differential geometry (especially complex differential geometry), such as the problem of finding metrics with optimal curvature properties, that can be approached by analysis of partial differential equations. I study real and complex Monge-Ampere equations, pluripotential theory, and geometric flows.
The Monge-Ampére equation with Guillemin boundary conditions, Calc. Var. and PDE, (2015) 1-18.