The Universal Structure of Moment Maps in Complex Geometry

Explore a mathematical seminar presentation where Mr. Michael Hallam from Aarhus Universitet delves into the universal structure of moment maps in complex geometry. Discover how canonical metrics, which are solutions to PDEs like the constant scalar curvature Kähler equation, Hermite-Einstein equation, and J-equation, emerge from moment maps on infinite dimensional spaces of metrics. Learn about groundbreaking research conducted with Ruadhaí Dervan that examines moment map properties through an equivariant cohomological lens, specifically by integrating equivariant forms over fibration fibers. Understand how this innovative approach requires only topological data input to naturally generate moment maps, and see practical applications in recovering geometric equations and other significant mathematical insights. Part of the "New equivariant methods in algebraic and differential geometry" event series, this hour-long presentation offers valuable insights into complex geometry's fundamental structures and their mathematical implications.