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My research topic is the construction of stability conditions on bounded derived category of coherent sheaves on projective varieties, which arises from the string theory in physics. In mathematics, we concern about the space of stability conditions on a fixed triangulated category, which was first introduced by Bridgeland. Moreover, it turns out that the theory of stability conditions has many connections with other areas, such as counting invariants and moduli space. It has been proved that Stab(X) is not empty when X is a curve or a surface. But it is still an open question whether Stab(X) is empty or not when dim X=3 and many interesting questions arise from it.