Explore the existence theory of minimal hypersurfaces in this 59-minute Members' Seminar presented by Fernando Marquez from Princeton University at the Institute for Advanced Study. Delve into key concepts such as the minimax theorem, space of cycles, and volume spectrum. Examine the minutes technique, boundary map theorem, and the implications of positive curvature and Ricci curvature. Investigate the fundamental college class, generic metrics, and general metrics. Gain insights into the topology of minimal hypersurfaces and engage with thought-provoking questions in this comprehensive lecture on advanced mathematical concepts.