My research is primarily concerned with studying geometry of algebraic varieties using homological algebraic methods. In particular, the theory of derived categories provides an effcient algebraic platform to investigate the“ hidden” geometric information of a variety. Also they have emerged as important objects in string theory. My recent research is focussed on constructing categorical stability conditions, and also studying associated moduli problems using Fourier-Mukai theory. I am also interested in investigating counting invariants on varieties and wall crossing phenomena.