Ask HN: Understanding inter-universal Teichmüller theory?
Hi! My name is Valera Rozuvan, and I want to understand inter-universal Teichmüller theory. For those of you who never heard of this theory, please take a look at the Wikipedia's entry https://en.wikipedia.org/wiki/Inter-universal_Teichm%C3%BCller_theory .
Why is this important? This theory might have a proof for the abc conjecture.
My background is in physics, optics. I finished the Taras Shevchenko National University of Kyiv. I am a hobbyist mathematician.
What should be my path of learning that will lead to understanding this theory? Any advice on specific texts, courses, online resources, etc. will be appreciated!
It would take an extraordinary effort. I doubt there is anyone who could learn this material given anything less than a year of solid study -- and I am thinking of the leading researchers in the world, who are already experts in everything related. I am a professional mathematician myself, and I doubt I could manage it even within a year.
This is dictated by the difficulty of the subject, and it is even more so since Mochizuki's papers are notoriously difficult to read. What I have heard from other research mathematicians is that Mochizuki doesn't make much of an effort to make himself comprehensible, to answer questions, or in general to explain his results to the community.
Also please be warned that the consensus is generally that Mochizuki's theory is probably incorrect.
That said, if you want to learn the stuff, there is no reference other than Mochizuki's papers themselves. If you would like to learn some general background theory I would recommend learning some algebraic geometry, for which see Ravi Vakil's book:
http://math.stanford.edu/~vakil/216blog/FOAGapr2915public.pd...
and maybe Milne on etale cohmology:
http://www.jmilne.org/math/CourseNotes/LEC210.pdf
If you find that incomprehensible, start with Dummit and Foote's Abstract Algebra (read it cover to cover), Neukirch's Algebraic Number Theory, Atiyah and Macdonald's Commutative Algebra, and Fulton and Harris's Representation Theory.
If you indeed want to read all that, you may as well enroll in a Ph.D. program in math....
see http://www.claymath.org/events/iut-theory-shinichi-mochizuki and https://www.maths.nottingham.ac.uk/personal/ibf/files/symcor... for more information, including the 1st letter to its participants.
hi there, you might start with this mathoverflow thread: http://mathoverflow.net/questions/106560/philosophy-behind-m...
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A very-very good YouTube video explaining what the abc conjecture is: https://www.youtube.com/watch?v=RkBl7WKzzRw .