Moment maps and geometric invariant theory

TL;DR

This paper explores the Kempf-Ness theorem linking symplectic and algebraic quotients, discusses invariant theory in tensor products, and reviews Teleman's enhancement of the quantization-reduction correspondence.

Contribution

It provides a comprehensive overview of the interplay between moment maps, geometric invariant theory, and recent advancements in quantization techniques.

Findings

Kempf-Ness theorem establishes quotient equivalences

Connections between invariant theory and tensor product invariants

Teleman's improved quantization and reduction results

Abstract

These lectures centered around the Kempf-Ness theorem, which describes the equivalence between notions of quotient in symplectic and algebraic geometry. The text also describes connections to invariant theory, such existence of invariants in tensor products of simple GL(r)-modules, and Teleman's improved version of quantization commutes with reduction.