# Kempf-Ness theorem

##
Yoshinori Hashimoto

created by daniele on 06 Jun 2018

modified on 11 Jun 2018

25 jun 2018
-- 10:00

Aula Tricerri, DiMaI, Firenze

**Abstract.**

This is an expository talk in which I explain the Kempf-Ness theorem for smooth projective varieties acted on by a reductive group, which states that the stability in the sense of Geometric Invariant Theory, a concept in algebraic geometry, is equivalent to the zero of the moment map in symplectic geometry. While its infinite dimensional analogues are much studied in recent years, with connections to Hermitian-Einstein or Kähler-Einstein metrics, in this talk we shall sketch the proof of this theorem for finite dimensional varieties. Most of the necessary concepts will be defined in the talk, including the basic notions in Geometric Invariant Theory, but some familiarity with Hamiltonian vector fields will be assumed.