Explore the intricate geometry of 2-dimensional Riemannian disks and spheres in this Members' Seminar presented by Regina Rotman from the University of Toronto. Delve into topics such as the proof of geodesics, sweep out techniques, round sphere properties, and curve shortening processes. Examine a specific example and problem, followed by its solution, to gain a deeper understanding of these geometric concepts. This hour-long lecture, delivered at the Institute for Advanced Study, offers valuable insights for mathematicians and geometry enthusiasts alike.