Gauss-Bonnet Formula for Renormalized Area of Minimal Submanifolds in Poincaré-Einstein Spaces
Explore a lecture on the Gauss-Bonnet formula for renormalized area of minimal submanifolds in Poincaré-Einstein spaces. Delve into the derivation process, which introduces several new mathematical concepts including a special compactification from scattering theory, conformally invariant powers of the Laplacian, Q-curvature on submanifolds of conformal manifolds, and a conjectured analog of Alexakis' result on conformally invariant integral integrands. Gain insights from Robin Graham's joint work with Jeffrey Case, Tzu-Mo Kuo, Aaron Tyrrell, and Andrew Waldron. Understand the context of this talk within the SCREAM project, focusing on Cartan and parabolic geometries and their applications in various fields such as mechanical systems, integrable systems theory, and Penrose's Conformal Cyclic Cosmology programme.