A surprising connection between symplectic geometry and geometric invariant theory

Speaker: 

Rumi Salazar

Affiliation: 

UNSW Sydney

Date: 

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

Venue: 

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

Abstract: 

 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.
 

School Seminar Series: