Speaker：Guokuan Shao (Sun Yat-sen University)

Time：2025-4-24, 16:30

Location：Conference Room S207 at Experiment Building at Haiyun Campus

Abstract:

In this talk I will first review the principle that “quantization commutes with reduction” ([Q, R]=0) for symplectic manifolds. Then I will discuss the [Q, R]=0 principle for complex manifolds with boundary. An important difference between the complex manifolds with boundary setting and the symplectic setting is that the quantum spaces in the case of compact symplectic manifolds are finite dimensional, whereas the quantum spaces consisting of holomorphic functions smooth up to the boundary for the compact complex manifolds with boundary are infinite dimensional. We will present that under natural pseudoconvexity assumptions that the Guillemin-Sternberg map is Fredholm. The main ingredient is asymptotics of G-invariant Bergman kernels.