Explore the intricate world of black hole stability through the lens of global and microlocal analysis in this comprehensive lecture by Andras Vasy from Stanford University. Delve into advanced mathematical concepts and techniques used to study the complex behavior of black holes, gaining insights into their stability properties and the analytical methods employed in modern gravitational physics research. Learn how global and microlocal analysis contribute to our understanding of these enigmatic cosmic phenomena, and discover the latest developments in this cutting-edge field of study.