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 topics over the course of 1 hour and 50 minutes: light condensed abelian groups, analytic rings, analytic stacks, and illustrative examples. Gain insights into cutting-edge approaches that aim to reshape the understanding of analytic geometry and its underlying structures.