School of Mathematical Sciences Academic Report [2025] 056  

(High-Level University Construction Series Report No. 1078)  

Lecture Title: Lagrangian Intersection, Symplectic Reduction and Kirwan Map  

Speaker: Dr. Ying Xie (Southern University of Science and Technology)  

Date & Time: 3:40 PM – 4:40 PM, June 24, 2025  

Venue: Room 1420, Convergence Building  

Abstract: 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.

Biography: Ying Xie, Postdoctoral Researcher at SUSTech, obtained her Ph.D. from The Chinese University of Hong Kong. Specializing in algebraic geometry, her research has been published in the J. Eur. Math. Soc..  

All faculty and students are welcome to attend!  

Invited by: Cong Ding  

School of Mathematical Sciences  

June 24, 2025