My mathematical research is focused on various subjects in complex algebraic geometry and Kähler geometry. The central objects that we study in complex algebraic geometry and Kähler geometry are complex projective varieties and Kähler manifolds.

Compact Kähler manifolds are natural generalizations of smooth projective varieties from the point of view of Hodge theory and deformation theory. In Kähler geometry, a basic problem that motivates my research work and ongoing projects is how general compact Kähler manifolds are in comparison to smooth projective varieties. In complex algebraic geometry, I study projective varieties through their subvarieties and more generally, their algebraic cycles. There are important and difficult conjectures about algebraic cycles such as the Hodge conjecture and the Bloch-Beilinson conjecture, predicting their existence and their connection with the topology of the variety. Among the projective varieties, I am particularly interested in K-trivial varieties, such as hyper-Kähler and Calabi-Yau manifolds. These varieties stand at the crossroads of various research areas in not only algebraic geometry, but also geometry in general as well as theoretical physics.