Editing Invariant theory (section)

== Geometric invariant theory ==
The modern formulation of [[geometric invariant theory]] is due to [[David Mumford]], and emphasizes the construction of a quotient by the group action that should capture invariant information through its coordinate ring. It is a subtle theory, in that success is obtained by excluding some 'bad' orbits and identifying others with 'good' orbits. In a separate development the [[symbolic method of invariant theory]], an apparently heuristic combinatorial notation, has been rehabilitated.

One motivation was to construct [[moduli space]]s in [[algebraic geometry]] as quotients of schemes parametrizing marked objects. In the 1970s and 1980s the theory developed 
interactions with [[symplectic geometry]] and equivariant topology, and was used to construct  moduli spaces of objects in [[differential geometry]], such as [[instanton]]s and [[monopole (mathematics)|monopoles]].