Moduli of G-bundles as a Quotient by the Gauge Group - Talk 6

Moduli of G-bundles as a Quotient by the Gauge Group - Talk 6

Explore a mathematical seminar talk that delves into the complex geometric description of holomorphic G-bundles and their relationship with gauge transformations. Learn how to interpret the moduli space of G-bundles through the lens of infinite-dimensional symplectic quotients, drawing parallels to the Kempf-Ness Theorem. Examine the Yang-Mills functional's role as a moment map norm and discover how the Harder-Narasimhan filtration connects to equivariant Morse theory. Understand Atiyah-Bott's methodology for computing cohomology of semistable G-bundle moduli spaces through an advanced mathematical discussion that bridges complex geometry, gauge theory, and algebraic topology.