MOMENT MAP AND CONVEX FUNCTION
时间  Datetime
2024-03-13 16:00 — 17:00
地点  Venue
会议室(703)
报告人  Speaker
Xiao Wei Wang
单位  Affiliation
Rutgers University at Newark
邀请人  Host
高云
备注  remarks
报告摘要  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 o 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. It is joint work with King-Leung Lee and Jacob Sturm.
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FROM 202.120.11.*