Explore new foundations for analytic geometry in this comprehensive lecture by Peter Scholze from MPIM Bonn, delivered at the Institut des Hautes Etudes Scientifiques (IHES). Delve into advanced mathematical concepts including light condensed abelian groups, analytic rings, and analytic stacks. Gain insights through practical examples provided throughout the nearly two-hour presentation. Enhance your understanding of cutting-edge developments in analytic geometry and their potential applications in mathematical research.