I work in geometric analysis and complex differential geometry, especially in Kähler geometry and nonlinear geometric PDE. Broadly speaking, I am interested in the way curvature, canonical metrics, and analytic structure constrain the global geometry of complex manifolds.
Much of my work concerns canonical Kähler metrics, complex Monge–Ampère and Hessian equations, rigidity and comparison questions for positively curved Kähler manifolds, and problems at the interface of analysis, algebraic geometry, and gauge theory.
Before coming to IISc, I was an RTG postdoctoral scholar at UC Berkeley and a visiting instructor at the University of Notre Dame. I completed my PhD at Rutgers University under Jian Song.
Research interests
Geometric analysis; Kähler geometry; complex differential geometry; canonical metrics; complex Monge–Ampère and Hessian equations; comparison and rigidity problems; and interactions with algebraic geometry and gauge theory.