爱情岛论坛 学术报告[2025]056号

(高水平大学建设系列报告1078号)

报告题目: Lagrangian Intersection, Symplectic Reduction and Kirwan Map

报告人：谢颖 （南方科技大学）

报告时间：2025年6月24日 3：40-4：40

讲座地点：汇文楼1420

报告内容：For a smooth holomorphic symplectic variety $X$ with a Hamiltonian action by a linearly reductive group $G$, the symplectic quotient $X//G$ is a 0-shifted symplectic stack, and $G$-invariant Lagrangians $C's$ induce Lagrangians in $X//G$.

In this talk, I will present a structure result for the derived intersection of two cleanly intersecting $G$-invariant Lagrangians $C_1, C_2$, and this leads to an isomorphism between the equivariant Ext groups of $C_1$ by $C_2$ in $X// G$ and the equivariant cohomology of $C_1\cap C_2$ under certain mild conditions on determinant of the normal bundle and properness of $C_1\cap C_2$. If the group action is linearized, then the functorial restriction from these Ext groups to those of their semi-stable GIT quotients is equivariant to Kirwan's map. This is a joint work with Conan Leung and Tony Yau.

报告人简介：谢颖，博士毕业于香港中文大学，现于南方科技大学从事博士后研究，研究方向为代数几何，论文发表在J. Eur. Math. Soc.等知名学术期刊。

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