Explore new foundations for analytic geometry in this comprehensive lecture by Peter Scholze from MPIM Bonn. Delve into light condensed abelian groups, analytic rings, and analytic stacks, with practical examples provided. Gain insights into cutting-edge mathematical concepts over the course of 1 hour and 46 minutes, as part of a series presented by the Institut des Hautes Etudes Scientifiques (IHES).