Derived Grassmannians and Instantons on Surface Blowups

Derived algebraic geometry allows us to extend Grothendieck’s theory of Grassmannians for quasi-coherent sheaves to the broader context of connective complexes. The framework of derived Grassmannians provides powerful tools for studying moduli spaces and their wall-crossings. Moreover, it yields unified structural results—for example, we obtained a single formula for the derived categories of Grassmannians associated to two-term perfect complexes of positive rank.

 

In this talk, I will discuss the representation-theoretic structures underlying these derived Grassmannians. As an application, I will address a question of Vafa–Witten concerning the representation-theoretic interpretation of the blowup formula for instanton moduli spaces on surface blowups. This is based on joint work with Weiping Li and Yu Zhao.