I wonder what Mochizuki's inter-universal geometry and his generalisation of anabelian geometry is, e.g. why the ABC-conjecture involves nested inclusions of sets as hinted in the slides, or why such inclusion structures should be simpler if they are between categories , how that relates to F_1. It seems to me that his basic idea is that algebraic geometry has in general a kind of semantic feedback-loop, what sounds very beautifull, if it were true. His view of Grothendieck/Deligne's idea of using the section conjecture for indirect proving finiteness statements seems to me as if he would say "The first part of that is just the first jump into the feedback-loop".
Edit: A nice link was jut given in: Mochizuki's proof and Siegel zeros
Edit: A relatively new survey