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Explore the foundations of Lorentzian geometry in this comprehensive lecture, covering essential topics from basic definitions and vector concepts to advanced subjects like Margulis space-times and crooked planes. Delve into models of hyperbolic spaces, isometries, and three-dimensional geometries while gaining insights into hyperbolic affine transformations and proper actions. Examine the Margulis Opposite Sign Lemma and its applications, and investigate the properties of crooked domains. Gain a thorough understanding of key results in this field of mathematics through clear explanations and in-depth analysis.
