Time：14:00-17:00, Wednesday, February 26 2025
Venue：E4-201
Host：Jiyuan Han, ITS
Speaker：Xiaowei Wang, Rutgers University
Title：MOMENT MAP AND CONVEX FUNCTION
Abstract：The concept moment map plays a central role in the study of Hamiltonian actions of compact Lie groups K on symplectic manifolds (Z, ω). In this talk, we propose a theory of moment maps coupled with an AdK-invariant convex function f on k∗, the dual of Lie algebra of K, and study the structure of the stabilizer of the critical point of f ◦ μ with moment map μ : Z → k∗. As an outcome, we are able to obtain a Calabi-Matsushima decomposition in this new framework. This work is motivated by the work of Donaldson on Ding functional, which is an example of infinite dimensional version of our setting. In particular, we obtain a natural interpretation of Tian-Zhu's generalized Futaki-invariant and Calabi-decomposition.
