A surprising connection between symplectic geometry and geometric invariant theory


Rumi Salazar


UNSW Sydney


Wed, 12/08/2020 - 12:00pm


Zoom link: https://unsw.zoom.us/j/92973609046


 In the 1980s, a relationship was found between the two fields of symplectic geometry and geometric invariant theory (GIT) via the Kempf-Ness theorem. Symplectic geometry generalises the notion of the phase space in classical mechanics, while GIT studies quotients by group actions in algebraic geometry.
In this talk, we give a brief overview of both symplectic geometry and GIT with the intent to discuss a corollary of the Kempf-Ness theorem. The corollary is the following: Given a smooth complex projective variety X and a complex reductive Lie group G, the GIT quotient of X by G is homeomorphic to the symplectic reduction of X by a maximal compact subgroup of G.

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