Pure Maths Colloquium: Symplectic implosion and non-reductive group actions
1 June 2009 16:15 in CM221
The symplectic reduction of a Hamiltonian action of a Lie group on a symplectic manifold plays the role of a quotient construction in symplectic geometry. It has been understood for several decades that symplectic reduction is closely related to the quotient construction for complex reductive group actions in algebraic geometry provided by Mumford's geometric invariant theory (GIT). Symplectic implosion (due to Guillemin, Jeffrey and Sjamaar) is much more recent, and is related to a generalised version of GIT which provides quotients for non-reductive group actions in algebraic geometry. The aim of this talk is to give a brief survey of symplectic reduction and symplectic implosion and their relationship with GIT, and (if time permits) describe an application of non-reductive GIT to Demailly's theory of jet differentials.
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