國立清華大學 數學系

Abstract:
In this talk, I will briefly review the classical theory of Hamiltonian G-spaces and symplectic reduction, illustrated with fundamental examples. Following this, I will introduce a related framework known as quasi-Hamiltonian G-spaces. In this setting, the classical moment map, which takes values in the dual of the Lie algebra, is replaced by a moment map taking values in the Lie group G itself. This theory admits an analogous reduction theorem that plays a significant role in gauge theory, particularly concerning the Atiyah-Bott symplectic structure on the moduli spaces of flat connections. To keep the presentation accessible, I will ground these concepts in concrete geometric examples throughout the talk.