I study the existence problem of canonical metrics on polarized manifolds by means of geometric analysis and algebraic geometry. Specifically, I study dynamical systems like geometric flows, and how they converge or blow up as time goes to infinity. This is purely a problem of geometric analysis. However, since any polarized manifold can be embedded into a projective space, we can study the problem from the view point of algebraic geometry. In this vein, my research theme lies at the intersection of geometry, analysis and algebra, owing to the rich geometry of manifolds.

Keywords	Complex Geometry, Algebraic Geometry, Non-Linear Elliptic/Parabolic PDE
Faculty , Department	Faculty of Mathematics , Department of Mathematics