MATD26H3

Geometric Analysis and Relativity

An intuitive and conceptual introduction to general relativity with emphasis on a rigorous treatment of relevant topics in geometric analysis. The course aims at presenting rigorous theorems giving insights into fundamental natural phenomena. Contents: Riemannian and Lorentzian geometry (parallelism, geodesics, curvature tensors, minimal surfaces), Hyperbolic differential equations (domain of dependence, global hyperbolicity). Relativity (causality, light cones, inertial observes, trapped surfaces, Penrose incompleteness theorem, black holes, gravitational waves).