*时间：2024年4月8日  13：30-14：25

*地点：数学楼401室

*主讲人：姜清元 助理教授（香港科技大学）

*主持人：杜荣 教授

*讲座内容简介：

Derived Algebraic Geometry (DAG) allows us to extend Grothendieck's theory of projectivizations and Grassmannians from sheaves to complexes. This extension proves valuable for constructing and studying moduli spaces, especially in the presence of singularities. In this talk, we discuss the construction and properties of derived projectivizations and Grassmannians. Furthermore, we provide structural results for their derived categories, revealing a unifying formula that simultaneously extends the important formulas for projective and Grassmannian bundles, blowups, standard flips, Grassmannian flips, and more. Moreover, we discuss this framework’s applications such as to Abel maps for singular curves and Hecke correspondences.

*主讲人简介：

姜清元，香港科技大学 助理教授，2018年在香港中文大学获得博士学位，主要从事研究领域包括 Derived Algebraic Geometry, Derived Categories, Bridgeland Stability Conditions, Donaldson–Thomas Theory, Geometric Representation Theory, Fargues–Fontaine Curves, p-adic Hodge Theory. 相关工作发表在J. Eur. Math. Soc.、Adv. Math.、Int. Math. Res. Not. 、J. Inst. Math. Jussieu. 等重要数学期刊上。