Mochizuki now hopes to solve the Riemann Hypothesis
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Anonymous2015-01-24 3:56
Go Yamashita is writing an independent survey of 200~300 pages in length about IUTeich and its initial results. Hopefully that will give a big boost for its study. Should be ready in about 2 or 3 months.
Acknowledgement The author cannot express enough his sincere and deep gratitude to Professors Shinichi Mochizuki and Kirti Joshi. Without their philosophies and amazinginsights, his study of mathematics would have remained “dormant”. The author deeply appreciates Professor Yuichiro Hoshi giving him helpful suggestions, as well as reading preliminary versions of the present paper. Butthe author alone, of course, is responsible for any errors and misconceptions in the present paper. Also, the author would also like to thank Professor Go Yamashita, Mr. Katsurou Takahashi (for giving him heartfelt encouragements), and the various individuals (including pointed stable curves of positive characteristic!) with whom the author became acquainted in Kyoto. The author means the present paper for a gratitude letter to them.
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Anonymous2015-01-24 3:57
Looks like Chung Pang Mok is giving some seminars on the USA.
Introduction to Mochizuki's works on inter-universal Teichmuller theory
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Anonymous2015-01-24 3:58
>>4 Not only on Mathematical Sciences Research and UC Santa Cruz, but he's also going to give lectures at University of British Columbia and Duke University.
Chung Pang Mok is definitely helping disseminate IUTeich in the USA.
I hope it begins to be taught all over the world so Mochizuki can focus on the Riemann Hypothesis.
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Anonymous2015-01-24 3:58
What is Mochizuki claiming, exactly? That he has a new set of techniques, which he calls “inter-universal geometry”, generalizing the foundations of algebraic geometry in terms of schemes first envisioned by Grothendieck? And that these new theory is useful in many ways, including solving the abc conjecture and possibly the Riemann Hypothesis? Huge!
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Anonymous2015-01-24 3:59
What are the pre-requisites in order to read the IUTeich papers?
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Anonymous2015-01-24 4:00
>>7 Hartshorne's Algebraic Geometry, a few analytic and algebraic number theory things and probably some of Grothendieck's work (EGA, SGA). Ask an expert in the field of arithmetic geometry, they would know more than me.
So can any mathematician understand this guy's work? I heard recently about Mochizuki complaining that other mathematicians are really struggling to understand what he has done.
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Anonymous2015-01-24 4:01
>>9 Read his report about the status of the theory:
Not completely related, but does anyone know if there is a version of the Pontryagin duality on varieties?
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Anonymous2015-01-24 4:02
>>11 There's Cartier duality, which is like Pontryagin duality for group schemes.
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Anonymous2015-01-24 4:03
What role do moduli spaces play in this theory? Teichmüller theory is all about them, right? But then again, isn't Teichmüller theory not about complex Riemannian surfaces? That's weird, I don't see how this theory would be analogous.
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Anonymous2015-01-24 4:04
>>13 A moduli space is a space that parametrizes a family of distinct objects (e.g. the triangles in the plane, distinguished up to rigid motion). Teichmuller space is the moduli space of all complex structures on a given space (e.g. a torus), up to homeomorphism (in the connected component of the identity). This itself turns out to be a complex manifold. The case of the torus (i.e. elliptic curves) is the easiest to start off with, if I recall correctly this is given by the torus's lattice in ℂ modulo rigid motions.
