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

Edit: Mochizuki' report on the current review status. Someone told me that there may be a seminar in Harvard on this next year.

Edit: New short survey by Ivan Fesenko :" This text is expected to help its readers to gain a general overview of the theory and a certain orientation in it, as well as to see various links between it and existing theories. Together with several mathematicians, we hope to organise a workshop in Europe, as well as an international conference in Kyoto in the summer of 2016. Feel free to contact me if you are interested to seriously study this work."