Appears in collection : Recent Advances in the Spherical Cap Conjecture

This mini-course, tled Recent Advances in the Spherical Cap Conjecture, will consist of six lectures, each lasng 1.5 hours, totaling 9 hours. The course aims to provide a comprehensive introducon to the Spherical Cap Conjecture, a central problem in classical differenal geometry concerning CMC surfaces with a circular boundary. At least half of the content (Lectures 1–3) is craed to be accessible to students beginning a Master's program, covering foundaonal concepts, historical context, and key techniques in an intuive manner. The remaining lectures (4–6) delve into advanced analycal methods and recent results, targeng doctoral students and researchers. The course combines geometric intuion with rigorous analycal tools.