Explore new foundations for analytic geometry in this comprehensive lecture by Peter Scholze at the Institut des Hautes Etudes Scientifiques (IHES). Delve into four key topics: light condensed abelian groups, analytic rings, analytic stacks, and relevant examples. Over the course of 1 hour and 46 minutes, gain insights into this advanced mathematical subject presented by the renowned mathematician. Enhance your understanding of analytic geometry and its potential applications in this in-depth academic presentation, featuring additional contributions from Dustin Clausen of IHES.