Notre Dame Professor of Mathematics
Ph.D., Imperial College London, 2006
BA, Cambridge University, UK, 2002
Analysis and Partial Differential Equations, Differential Geometry
Complex and Partial Differential Geometry
My research interests are in geometric analysis and complex geometry. More specifically I am interested in questions related to finding canonical metrics on Kähler manifolds, and the relation to alebro-gemetric stability conditions. This involves problems of nonlinear partial differential equations related to the real and complex Monge-Ampère equations and also algebraic problems coming from geometric invariant theory.
- On blowing up extremal Kähler manifolds, arXiv:1010.5130
- (with O. Munteanu) On convergence of the Kähler-Ricci flow, arXiv:0904.3505
- (with J. Stoppa) Relative K-stability of extermal metrics, arXiv:0912.4095, to appear in J. Eur. Math. Soc.
- (with V. Tosatti) Regularity of weak solutions of a complex Monge-Ampère equation, arXiv:0912:1808, to appear in Analysis & PDE
- Greatest lower bounds on the Ricci curvature of Fano manifolds, arXiv:0903.5504, to appear in Compositio Math.