Symmetric Trilinear Forms and Einstein-like Equations: From Affine Spheres to Griess Algebras
Offered By: Centrum Fizyki Teoretycznej PAN via YouTube
Course Description
Overview
Explore a comprehensive lecture on symmetric trilinear forms and Einstein-like equations, spanning from affine spheres to Griess algebras. Delve into the concept of Einstein-like equations in the context of coupling metrics to tensors with prescribed symmetries. Examine a hierarchy of equations generalizing constant sectional curvature, Einstein, and constant scalar curvature. Review affine differential geometry of nondegenerate hypersurfaces and discover a class of geometric structures that extend statistical and Weyl structures. Investigate Einstein equations that generalize Einstein-Weyl equations and their relationship to affine spheres. Uncover further examples through algebraic constructions, including discussions on metrized commutative algebras akin to simple Jordan algebras and Griess algebras of VOAs. Gain insights into the unifying element of these diverse contexts: symmetric trilinear forms. This lecture is part of the SCREAM project, focusing on Cartan and parabolic geometries and their interactions with mechanical systems, integrable systems, and Penrose's Conformal Cyclic Cosmology programme.
Syllabus
Symmetric trilinear forms and Einstein-like equations: from affine spheres to Griess algebras
Taught by
Centrum Fizyki Teoretycznej PAN
Related Courses
Geometry of Quantum Correlations - Part IICentrum Fizyki Teoretycznej PAN via YouTube Geometry of Quantum Correlations
Centrum Fizyki Teoretycznej PAN via YouTube Gauss-Bonnet Formula for Renormalized Area of Minimal Submanifolds in Poincaré-Einstein Spaces
Centrum Fizyki Teoretycznej PAN via YouTube Dispersionless Integrable Equations and Modular Forms
Centrum Fizyki Teoretycznej PAN via YouTube Applications of Tractor Calculus in General Relativity - Part I
Centrum Fizyki Teoretycznej PAN via YouTube