Explore new foundations for analytic geometry in this 1 hour 45 minute lecture by Peter Scholze from the Max Planck Institute for Mathematics in Bonn. Delve into advanced mathematical concepts including light condensed abelian groups, analytic rings, and analytic stacks. Gain insights through practical examples that illustrate these complex topics. This lecture, part of a series at the Institut des Hautes Etudes Scientifiques (IHES), offers a deep dive into cutting-edge research in analytic geometry, providing valuable knowledge for mathematicians and researchers in related fields.