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 nearly two hours: light condensed abelian groups, analytic rings, analytic stacks, and illustrative examples. Gain insights into cutting-edge mathematical concepts and their applications in analytic geometry as presented by a renowned expert in the field.