Explore new foundations for analytic geometry in this comprehensive lecture by Dustin Clausen at the Institut des Hautes Etudes Scientifiques (IHES). Delve into four key areas over the course of 2 hours and 10 minutes: light condensed abelian groups, analytic rings, analytic stacks, and relevant examples. Gain insights into cutting-edge concepts that aim to reshape the understanding of analytic geometry and its applications in advanced mathematical research.