Research Interests: 

My research area is algebraic geometry with a particular focus on the derived category of coherent sheaves on quasi-projective varieties. Algebraic geometry studies geometric objects defined by polynomial equations, known as varieties. The derived category associated with the variety provides a linear tool for understanding the nonlinear structure in geometry.

My works explore several interconnected topics. Along one direction, I study Bridgeland stability condition, which is a stability condition defined on the derived category of coherent sheaves on an algebraic variety. Our recent work contributes to the understanding of Bridgeland stable objects. In many cases, the stable objects form a well-behaved topological space called the moduli space. By performing intersection theory on this moduli space, one can derive enumerative invariants of the variety, such as the famous result that a cubic surface contains exactly 27 lines. My other research direction focuses on a "categorified" enumerative theory–motivic Donaldson-Thomas theory. 


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