Cartan Geometry and Infinite-Dimensional Kempf-Ness Theory

Explore a groundbreaking lecture on the development of an infinite-dimensional framework for the Kempf-Ness theorem, addressing challenges in symmetry group complexification. Delve into a novel approach using Cartan bundles to generalize Kempf-Ness theory, emphasizing the crucial role of Cartan connections. Learn how this framework defines and examines key elements like complex orbit models and the Kempf-Ness functional, while establishing convexity properties and identifying obstructions to moment map zeros. Discover applications of this innovative approach in Kähler geometry, deformation quantization, and gauge theory, based on collaborative research with Tobias Diez and Tudor S. Ratiu.

Akito Futaki: Cartan Geometry and Infinite-Dimensional Kempf-Ness Theory #ICBS2024