（前“応援”スレが、1000又は1000近くになったので、新スレ立てる） 前スレ：Inter-universal geometry と ABC予想 (応援スレ) 70 https://rio2016.5ch.net/test/read.cgi/math/1701399491/ 詳しいテンプレは、下記旧スレへのリンク先ご参照 Inter-universal geometry と ABC予想 (応援スレ) 52 https://rio2016.5ch.net/test/read.cgi/math/1613784152/1-13 ＜IUT最新文書＞ https://www.kurims.kyoto-u.ac.jp/~motizuki/news-japanese.html 2024年03月24日 望月新一 ・（過去と現在の研究）2024年4月に開催予定のIUGCの研究集会での講演の スライドを公開。https://www.kurims.kyoto-u.ac.jp/~motizuki/IUT%20as%20an%20Anabelian%20Gateway%20(IUGC2024%20version).pdf P8 In this context, it is important to remember that, just like SGA, IUT is formulated entirely in the framework of “ZFCG” (i.e., ZFC + Grothendieck’s axiom on the existence of universes), especially when considering various set-theoretic/foundational subtleties (?) of “gluing” operations in IUT (cf. [EssLgc], §1.5,§3.8,§3.9, as well as [EssLgc],§3.10, especially the discussion of “log-shift adjustment” in (Stp 7)): (引用終り)
https://www3.nhk.or.jp/news/html/20230707/k10014121791000.html NHK 数学「ABC予想」新たな証明理論の研究発展させる論文に賞創設 20230707 数学の難問「ABC予想」を証明したとする日本の数学者の新たな理論をめぐって、研究を発展させる論文を対象に、100万ドルの賞金を贈呈する賞が国内のIT企業の創業者によって創設されることになりました。 ▽新たな発展を含む論文を毎年選び、最大で賞金10万ドル ▽理論の本質的な欠陥を示す論文を発表した最初の執筆者に対しては100万ドルを、 それぞれ贈呈するとしています。
https://ahgt.math.cnrs.fr/activities/ Anabelian Geometry and Representations of Fundamental Groups. Oberwolfach workshop MFO-RIMS Sep. 29-Oct. 4, 2024 Org.: A. Cadoret, F. Pop, J. Stix, A.. Topaz （J. Stixさん、IUT支持側へ）
>>210 >The essential difference here compared to the case of a body is that, in general, the injectivity of a linear mapping no longer results in its surjectivity (and thus its bijectivity), as in the simple example Z →Z, x→ 2x shows. ここ、１は全くワケワカランだろうから解説する
良い質問だ https://en.wikipedia...ombinatorial_species Combinatorial species Category theory provides a useful language for the concepts that arise here, but it is not necessary to understand categories before being able to work with species. The category of species is equivalent to the category of symmetric sequences in finite sets.[1]
https://www.kurims.k...er%20Theory%20IV.pdf [4] Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations. (2020-04-22) P67 Section 3: Inter-universal Formalism: the Language of Species In the present §3, we develop — albeit from an extremely naive/non-expert point of view, relative to the theory of foundations! — the language of species. Roughly speaking, a “species” is a “type of mathematical object”, such as a ”group”, a “ring”, a “scheme”, etc. In some sense, this language may be thought of as an explicit description of certain tasks typically executed at an implicit, intuitive level by mathematicians [i.e., mathematicians who are not equipped with a detailed knowledge of the theory of foundations!] via a sort of “mental arithmetic” in the course of interpreting various mathematical arguments. In the context of the theory developed in the present series of papers, however, it is useful to describe these intuitive operations explicitly.
論文 IUT VI https://www.kurims.k...er%20Theory%20IV.pdf [4] Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations. (2020-04-22)
これで”species”の単語検索すると P1からP7 でなど ”If,instead of working species-theoretically, one attempts to document all of the possible choices that occur in various newly introduced universes that occur in a construction,” ときて、その後P67 まで無しで ”Section 3: Inter-universal Formalism: the Language of Species”へジャンプなんだ
https://twitter.com/math_jin math_jin 4h Submitted 29 April, 2024; （論文もアブストラクトも大幅に改訂！）
On Mochizuki's idea of Anabelomorphy and its applications Authors: Kirti Joshi #IUTabc
arxiv.org On Mochizuki's idea of Anabelomorphy and its applications I coined the term anabelomorphy (pronounced as anabel-o-morphy) as a concise way of expressing https://t.co略 https://twitter.com/thejimwatkins (deleted an unsolicited ad)
Response to Mochizuki’s comments on my papers Kirti Joshi April 30, 2024 P3 Summary All in all, I have believed, and asserted (in all my papers on this topic) that you have presented rather new ideas in Diophantine Geometry and I have shown that these ideas can be made precise using a new set of tools (especially my use of perfectoid fields and untilts in this context) which are better suited for this purpose than the ones you have created. (引用終り)
・私は、心情的には Kirti Joshi氏応援です ”using a new set of tools (especially my use of perfectoid fields and untilts in this context)” とあります。Scholze氏の”perfectoid”を”new set of tools”として使おうという ・成功するか失敗するか不明ですが 失敗でも何か意味ある結果が生まれますように ・例えば、山登りに例えると、望月IUT山がヒマラヤ級で8000ｍとして Scholze氏の”perfectoid”山が、5000ｍとして 5000ｍ地点から登れば楽になるとかね
・時計が4年くらい止まっている ・2024年4月は下記です Germany Jakob Stix、USA Florian Pop、Kiran Kedlaya、Jeff Lagarias 日本では、Ochiai Tadashi, Tokyo Institute of Technology、Toshiyuki Katsura（Tokyo） ・いまさら、”IUTを救う”とか噴飯もの ・「潰すなら潰して見せよホトトギス」と川上氏は、100万ドル（1.5億円）の懸賞金
https://ahgt.math.cnrs.fr/members/ Arithmetic & Homotopic Galois Theory IRN Members & Partners
The LPP-RIMS AHGT International Research Network is a France-Japan network between Laboratoire Paul Painlevé of Lille University -- Algebraic and arithmetic geometry & Geometry and Topology, the DMA of ENS Paris PSL, and RIMS of Kyoto University as leading institutions, which regroups 45 researchers and a dozen PhD students in 16 universities as core members.
The activity of the LPP-RIMS AHGT IRN is supported by 40 international researchers over 12 countries and 32 institutions. Within RIMS, the international center for next-generation geometry is a special partner of the LPP-RIMS AHGT network.
RIMS, Kyoto University Benjamin Collas
Lille University Pierre Dèbes
ENS Paris Ariane Mézard
Sorbonne University Emmanuel Lepage
Researchers Partners Germany Jakob Stix, Goethe-University Frankfurt
Japan Ochiai Tadashi, Tokyo Institute of Technology
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=13895 A Report From Mochizuki Posted on March 25, 2024 by woit
Unfollow says: May 2, 2024 at 5:20 am Will Sawin has already pointed out a flaw in Joshi’s response, here https://mathoverflow.net/questions/467696/global-character-of-abc-szpiro-inequalities#:~:text=I%20believe%20the%20claim,dealing%20with%22%20is%20wrong.
10 Will Sawin yesterday 略す
8 Thanks to Peter Scholze (by email) and Will Sawin for pointing this out. My discussion of Mochizuki's example is incorrect. Both the above linked files have been updated. – Kirti Joshi 18 hours ago
あ、本当だね mathoverflow/stackexchangeのWill Sawin Profilesでは ”I am an associate professor at Columbia University.”なのに 2024年からプリンストンの教授か Fernholz Professorで、Robert Fernholz氏関連かも
https://williamsawin.com/ I am a professor at Princeton University. My research relates to the applications of étale cohomology to analytic number theory via exponential sums, the slice rank method in combinatorics, equidistribution questions in algebraic number theory, and other areas.
Publications & Preprints Papers on arXiv Analytic number theory over function fields and étale cohomology
https://williamsawin.com/cv.pdf CURRICULUM VITAE Will Sawin Princeton University Fernholz Professor 2024- present Columbia University Associate Professor (tenured) 2023- 2023 Columbia University Assistant Professor (tenure-track) 2018- 2022
https://dof.princeton.edu/news/2023/faculty-members-named-endowed-professorships-2 princeton Faculty members named to endowed professorships Will Sawin, the Fernholz Professor of Mathematics, effective Jan. 1, 2024.
https://en.wikipedia.org/wiki/Robert_Fernholz Robert Fernholz Robert Fernholz (born Erhard Robert Fernholz, March 27, 1941) is a mathematician and financial researcher specializing in mathematics of finance. He founded INTECH, an institutional equity management firm, in 1987 where he was its chief investment officer. He is also the President of Allocation Strategies, LLC, a company that he founded in 2012. Alma mater Princeton University、Columbia University
Will Sawin Profiles https://stackexchange.com/users/2952423/will-sawin New York, NY, USA williamsawin.com I am an associate professor at Columbia University.
289 名前：)Cite Improve this answer Follow edited Dec 12, 2013 at 18:49 Will Sawin ii)2 That is quite a list of authors. – Will Sawin Oct 5, 2012 at 18:39 ですね。 ・補足すると、上記”ii)2”は、”answered Oct 5, 2012 at 7:45 Niels”へのコメントで ”i)Cite Improve ”は、Dec 12, 2013で １年後に思い出したようにFollowしている
追記 ・”1 users.ictp.it/~pub_off/lectures/lns001/Matsumoto/Matsumoto.pdf – Junyan Xu May 7, 2013 at 23:11 Add a comment” があるが、リンク切れ
おもろいオッサンやね １）recursive set＝Computable set かな ”if there is an algorithm which takes a number as input, terminates after a finite amount of time (possibly depending on the given number) and correctly decides whether the number belongs to the set or not.” だね？ ２)ところで、問題は「ある論文の証明を、定理証明システムに乗せて、コンピュータを走らせたとき、必ず停止するか？」ってことだよね 最初から”recursive set”を仮定するなら良いが、その仮定がないときは「必ず停止する」は言えないよｗ ３）ヒルベルト第10問題 ”Hilbert's tenth problem is not computable”だ 定理証明システムも、停止問題あるよ
(参考) https://en.wikipedia.org/wiki/Computable_set Computable set In computability theory, a set of natural numbers is called computable, recursive, or decidable if there is an algorithm which takes a number as input, terminates after a finite amount of time (possibly depending on the given number) and correctly decides whether the number belongs to the set or not. A set which is not computable is called noncomputable or undecidable. Examples and non-examples Non-examples: Main article: List of undecidable problems ・The set of Turing machines that halt is not computable. ・Hilbert's tenth problem is not computable.
https://en.wikipedia.org/wiki/Halting_problem Halting problem In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. The halting problem is undecidable, meaning that no general algorithm exists that solves the halting problem for all possible program–input pairs. （google訳） 計算可能性理論における停止問題とは、任意のコンピューター プログラムの記述と入力から、そのプログラムが実行を終了するか、それとも永久に実行し続けるかを判断する問題です。停止問題は決定不可能です。これは、考えられるすべてのプログラムと入力のペアに対して停止問題を解決する 一般的なアルゴリズムが存在しないことを意味します。
https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values. Hilbert's tenth problem has been solved, and it has a negative answer: such a general algorithm cannot exist.
(参考) https://ja.wikipedia.org/wiki/P%E2%89%A0NP%E4%BA%88%E6%83%B3 P≠NP予想 P≠NP予想（P≠NPよそう、英語: P is not NP）は、計算複雑性理論（計算量理論）における予想 (未解決問題) の1つであり、「クラスPとクラスNPが等しくない」すなわち「クラスNPの元だがクラスPの元でないような決定問題（判定問題）が存在する」というものである。P対NP問題（PたいNPもんだい、英: P versus NP）と呼ばれることもある。 理論計算機科学と現代数学上の未解決問題の中でも最も重要な問題の一つであり、2000年にクレイ数学研究所のミレニアム懸賞問題の一つとして、この問題に対して100万ドルの懸賞金がかけられた。 概要 クラスPとは、決定性チューリングマシンにおいて、多項式時間で判定可能な問題のクラスであり、クラスNPは、Yesとなる証拠（Witnessという）が与えられたとき、多項式時間でWitnessの正当性の判定（これを検証という）が可能な問題のクラスである。多項式時間で判定可能な問題は、多項式時間で検証可能であるので、P⊆NPであることは明らかであるが、PがNPの真部分集合であるか否かについては明確ではない。証明はまだないが、多くの研究者はP≠NPだと信じている。そして、このクラスPとクラスNPが等しくないという予想を「P≠NP予想」という。 []
