Spacetime G-structures I - Introduction to Klein Models and Associated Geometries

Explore the foundations of spacetime geometry in this lecture by Prof. José Figueroa-O'Farrill from the University of Edinburgh. Delve into the evolution of spacetime models, from Minkowski's Lorentzian manifold to Newtonian mechanics' Galilei spacetime and Lévy-Leblond's Carroll spacetime. Examine the Klein models for carrollian, galilean, and lorentzian geometries, and their significance in various areas of physics, including black holes and flat-space holography. Focus on the underlying geometries, introducing Klein models, associated G-structures, and their intrinsic torsion. Gain insights into the classification of these geometries and potential generalizations related to extended objects in string theory. This lecture is part of the SCREAM project, exploring Cartan and parabolic geometries and their interactions with mechanical systems, integrable systems, and cosmology.