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SUMMARY:Moment map and convex function - Xiaowei Wang  (Rutgers\, The Stat
 e University of New Jersey)
DTSTART:20240513T091500Z
DTEND:20240513T101500Z
UID:TALK214321@talks.cam.ac.uk
DESCRIPTION:The concept moment map plays a central role in the study of Ha
 miltonian actions of compact Lie groups $K$ on symplectic manifolds. In th
 is note\, we propose a theory of moment maps coupled with an $\\Ad_K$-inva
 riant convex function $f$ on $\\fk^\\ast$\, the dual of Lie algebra of $K$
 \, and study the structure of the stabilizer of the critical point of $f\\
 circ\\mu$. Our work is motivated by the work of Donaldson \\cite{Donaldson
 2017}\, which is an example of an infinite dimensional version of our sett
 ing. As an application\, we give a natural interpretation of Tian-Zhu's ge
 neralized Futaki-invariant and Calabi-decomposition.
LOCATION:Seminar Room 1\, Newton Institute
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