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Francis Kirwan: Lectures

January 10, 2022
TITLE: Hyperkahler implosion

ABSTRACT: The hyperkahler quotient construction, which allows us to construct new hyperkahler spaces from suitable group actions on hyperkahler manifolds, is an analogue of symplectic reduction (introduced by Marsden and Weinstein in the 1970s), and both are closely related to the quotient construction for complex reductive group actions in algebraic geometry provided by Mumford’s geometric invariant theory (GIT). Symplectic implosion was introduced twenty years ago by Guillemin, Jeffrey and Sjamaar; in some sense it abelianises symplectic reduction. Hyperkahler implosion is in turn an analogue of symplectic implosion; both are related to a generalised version of GIT providing quotients for non-reductive group actions in algebraic geometry.

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