Explore the intricacies of cosmic censorship conjectures in general relativity through this advanced lecture delivered by Mihalis Dafermos from Princeton University and the University of Cambridge. Delve into complex topics such as global high publicity, antitrapped surfaces, and null infinity as part of the ICTP School on Geometry and Gravity. Examine the lemma, I plus, and future not infinity concepts before investigating the Hawking pass and various matter models. Gain deep insights into this fundamental aspect of general relativity theory over the course of 78 minutes, suitable for graduate-level physics and mathematics students or researchers in the field.