IUT Wiki - User contributions [en]

Main Page

2016-09-19T06:28:21Z

Artur:

Welcome to the IUT Wiki: A Group Wiki for Shinichi Mochizuki's Inter-Universal Teichmüller Theory.

IUT Wiki was created to serve as a place for those currently independently evaluating, in a non-partisan manner, Shinichi Mochizuki's proof of the ABC conjecture to arrange ideas concerning the structure of Inter-Universal Teichmüller theory, its philosophies, and attendant questions. At this point is has become clear that many of the topics that comprise what Mochizuki calls Inter-Universal Teichmüller theory are mathematically interesting in their own right, apart from its main application: the ABC. A separate mission of the IUT Wiki is to explain in simpler words and sometimes alternative language some of these topics contained in Mochizuki's works, both in the IUT papers and before. This has the side effect that structure of the theory may be presented slightly differently than Mochizuki had originally.
If you are interested in contributing, please contact [http://iut.fpqc.net/wiki/index.php?title=User:Artur Artur Jackson] : artur [at] fpqc [dot] net.

Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.

Main Page

2016-09-19T02:31:37Z

Artur: Removed default junk.

Welcome to the IUT Wiki: A Group Wiki for Shinichi Mochizuki's Inter-Universal Teichmüller Theory.

IUT Wiki was created to serve as a place for those currently independently evaluating, in a non-partisan manner, Shinichi Mochizuki's proof of the ABC conjecture to arrange ideas concerning the structure of Inter-Universal Teichmüller theory, its philosophies, and attendant questions. At this point is has become clear that many of the topics that comprise what Mochizuki calls Inter-Universal Teichmüller theory are mathematically interesting in their own right, apart from its main application: the ABC. A separate mission of the IUT Wiki is to explain in simpler words and sometimes alternative language some of these topics contained in Mochizuki's works, both in the IUT papers and before. This has the side effect that structure of the theory may be presented slightly differently than Mochizuki had originally.
If you are interesting in contributing, please contact [http://iut.fpqc.net/wiki/index.php?title=User:Artur Artur Jackson] : artur [at] fpqc [dot] net.

Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.

User:Artur

2016-09-19T02:28:59Z

Artur:

I'm Artur Jackson, a Ph.D. student at Purdue University working in applications of homotopy theory to arithmetic geometry. I've been to the 2015 Oxford Workshop, visted RIMS to speak with Yuichiro Hoshi and Shinichi Mochizuki in March 2016, attended the 2016 Kyoto IUT Summit. In the US I've been to Taylor Dupuy and Christelle Vincent's "Kummer Classes and Anabelian Geometry" meeting in Burlington, Vermont. Currently I'm thinking about aspects of IUT viewed through the biased lens of <m>\mathbb{F}_1</m>-algebraic geometry.

Almost everything I've been able to learn about IUT has been from a combination of lectures and personal discussion from the following people: Shinichi Mochizuki, Yuichiro Hoshi, Chung Pang Mok, Taylor Dupuy, Emmanuel Lepage, Kiran Kedlaya, and Jeff Lagarias. I'd like to say thanks! The majority of these meetings were facilitated by [https://en.wikipedia.org/wiki/Ivan_Fesenko Ivan Fesenko]'s willingness to engage the mathematical community enough to pique their interest in Mochizuki's work and also his dedication to securing funding for these meetings. He definitely deserves a big thanks for this major contribution to the unrolling saga of the mathematics community coming to a consensus on the proof of the ABC conjecture.

IUT in Pop Culture

2016-09-19T01:48:57Z

Artur: Created page with "Shinichi Mochizuki and Inter-Universal Teichmüller Theory have made their way into a number of recent pop-articles. Here are a few of them: * [http://www.nature.com/news/the..."

Shinichi Mochizuki and Inter-Universal Teichmüller Theory have made their way into a number of recent pop-articles. Here are a few of them:

* [http://www.nature.com/news/the-biggest-mystery-in-mathematics-shinichi-mochizuki-and-the-impenetrable-proof-1.18509 The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof], in Nature, by David Castelvecchi.
* [http://www.nature.com/news/monumental-proof-to-torment-mathematicians-for-years-to-come-1.20342 Monumental proof to torment mathematicians for years to come], in Nature, by David Castelvecchi.
* [http://motherboard.vice.com/read/a-500-page-proof-offers-a-new-univers-if-only-mathematicians-could-understand-i The 500-Page Proof That Only One Mathematician Can Understand], on Vice Motherboard, by Michael Byrne.
* [http://motherboard.vice.com/read/mathematicians-closer-to-understanding-epic-400-page-proof Mathematicians Still Years from Verifying Nightmare 500-Page Proof], in Vice Motherboard, by Michael Byrne.

Main Page

2016-09-19T01:07:37Z

Artur:

Welcome to the IUT Wiki: A Group Wiki for Shinichi Mochizuki's Inter-Universal Teichmüller Theory.

IUT Wiki was created to serve as a place for those currently independently evaluating, in a non-partisan manner, Shinichi Mochizuki's proof of the ABC conjecture to arrange ideas concerning the structure of Inter-Universal Teichmüller theory, its philosophies, and attendant questions. At this point is has become clear that many of the topics that comprise what Mochizuki calls Inter-Universal Teichmüller theory are mathematically interesting in their own right, apart from its main application: the ABC. A separate mission of the IUT Wiki is to explain in simpler words and sometimes alternative language some of these topics contained in Mochizuki's works, both in the IUT papers and before. This has the side effect that structure of the theory may be presented slightly differently than Mochizuki had originally.
If you are interesting in contributing, please contact [http://iut.fpqc.net/wiki/index.php?title=User:Artur Artur Jackson] : artur [at] fpqc [dot] net.

Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [//www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
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Main Page

2016-09-19T01:05:48Z

Artur: Added intro bit. Copied from "About IUT Wiki" page.

Welcome to the IUT Wiki: A Group Wiki for Shinichi Mochizuki's Inter-Universal Teichmüller Theory.

IUT Wiki was created to serve as a place for those currently independently evaluating, in a non-partisan manner, Shinichi Mochizuki's proof of the ABC conjecture to arrange ideas concerning the structure of Inter-Universal Teichmüller theory, its philosophies, and attendant questions. At this point is has become clear that many of the topics that comprise what Mochizuki calls Inter-Universal Teichmüller theory are mathematically interesting in their own right, apart from its main application: the ABC. A separate mission of the IUT Wiki is to explain in simpler words and sometimes alternative language some of these topics contained in Mochizuki's works, both in the IUT papers and before. This has the side effect that structure of the theory may be presented slightly differently than Mochizuki had originally.
If you are interesting in contributing, please contact Artur Jackson: artur [at] fpqc [dot] net.

Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [//www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [//www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]
* [//www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]

User:Artur

2016-09-19T00:26:31Z

Artur:

I'm, Artur Jackson, a Ph.D. student at Purdue University working in applications of homotopy theory to arithmetic geometry. I've been to the 2015 Oxford Workshop, visted RIMS to speak with Yuichiro Hoshi and Shinichi Mochizuki in March 2016, attended the 2016 Kyoto IUT Summit. In the US I've been to Taylor Dupuy and Christelle Vincent's "Kummer Classes and Anabelian Geometry" meeting in Burlington, Vermont. Currently I'm thinking about aspects of IUT viewed through the biased lens of <m>\mathbb{F}_1</m>-algebraic geometry.

Almost everything I've been able to learn about IUT has been from a combination of lectures and personal discussion from the following people: Shinichi Mochizuki, Yuichiro Hoshi, Chung Pang Mok, Taylor Dupuy, Emmanuel Lepage, Kiran Kedlaya, and Jeff Lagarias. I'd like to say thanks! The majority of these meetings were facilitated by [https://en.wikipedia.org/wiki/Ivan_Fesenko Ivan Fesenko]'s willingness to engage the mathematical community enough to pique their interest in Mochizuki's work and also his dedication to securing funding for these meetings. He definitely deserves a big thanks for this major contribution to the unrolling saga of the mathematics community coming to a consensus on the proof of the ABC conjecture.

User:Artur

2016-09-19T00:14:39Z

Artur: Created page with "I'm, Artur Jackson, a Ph.D. student at Purdue University working in applications of homotopy theory to arithmetic geometry. I've been to the 2015 Oxford Workshop, visted RIMS..."

IUT Wiki:About

2016-09-18T23:27:45Z

Artur: Created page with "IUT Wiki was created to serve as a place for those currently independently evaluating, in a non-partisan manner, Shinichi Mochizuki's proof of the ABC conjecture to arrange id..."

IUT Wiki was created to serve as a place for those currently independently evaluating, in a non-partisan manner, Shinichi Mochizuki's proof of the ABC conjecture to arrange ideas concerning the structure of Inter-Universal Teichmüller theory, its philosophies, and attendant questions. At this point is has become clear that many of the topics that comprise what Mochizuki calls Inter-Universal Teichmüller theory are mathematically interesting in their own right, apart from its main application: the ABC. A separate mission of the IUT Wiki is to explain in simpler words and sometimes alternative language some of these topics contained in Mochizuki's works, both in the IUT papers and before. This has the side effect that structure of the theory may be presented slightly differently than Mochizuki had originally.

If you are interesting in contributing, please contact Artur Jackson: artur [at] fpqc [dot] net.

Frobenioid

2016-09-18T23:13:02Z

Artur:

A frobenioid structure on a category <m>\mathcal{C}</m> is a functor <m>\mathcal{C} \to \mathbb{F}_\Phi</m> satisfying certain properties to a special type of category called an elementary frobenioid. These were designed by Mochizuki to encapsulate and abstract the notions of coverings and divisors.

Frobenioid

2016-09-18T23:12:38Z

Artur: Created page with "A frobenioid structure on a category <m>\mathcal{C}</m> is a functor $\mathcal{C} \to \mathbb{F}_\Phi$ satisfying certain properties to a special type of category called an el..."

A frobenioid structure on a category <m>\mathcal{C}</m> is a functor $\mathcal{C} \to \mathbb{F}_\Phi$ satisfying certain properties to a special type of category called an elementary frobenioid. These were designed by Mochizuki to encapsulate and abstract the notions of coverings and divisors.

Main Page

2016-09-18T22:40:26Z

Artur:

Welcome to the IUT Wiki: A Group Wiki for Shinichi Mochizuki's Inter-Universal Teichmüller Theory.

Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [//www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [//www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]
* [//www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]