Inter-universal geometry と ABC予想 (応援スレ) 77

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 77 (1002ﾚｽ)
上下前次 1-新
通常表示 512ﾊﾞｲﾄ分割ﾚｽ栞

このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索歴削→次ｽﾚ栞削→次ｽﾚ過去ﾛｸﾞﾒﾆｭｰ

624: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2025/11/09(日) 16:02:17.60 ID:QrKJGO9s

>>537より 追加
https://en.wikipedia.org/wiki/Geometric_Langlands_correspondence
Geometric Langlands correspondence
Status
A claimed proof of the categorical unramified geometric Langlands conjecture was announced on May 6, 2024 by a team of mathematicians including Dennis Gaitsgory.[7][8]
The claimed proof is contained in more than 1,000 pages across five papers and has been called "so complex that almost no one can explain it".
Even conveying the significance of the result to other mathematicians was described as "very hard, almost impossible" by Drinfeld.[9]

Breakthrough Prize なんだね（下記）

https://en.wikipedia.org/wiki/Dennis_Gaitsgory
Dennis Gaitsgory (born 17 November 1973) is an Israeli-American mathematician. He is a mathematician at Max Planck Institute for Mathematics (MPIM) at Bonn and is known for his research on the geometric Langlands program.
Honors and awards
In 2025, he received the Breakthrough Prize in Mathematics.[3]

（Scholzeさん）
https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/
Quanta magazine
Monumental Proof Settles Geometric Langlands Conjecture
Erica Klarreich July 19, 2024
The proof represents the culmination of three decades of effort, said Peter Scholze(opens a new tab), a prominent mathematician at the Max Planck Institute for Mathematics who was not involved in the proof. “It’s wonderful to see it resolved.”
Dennis Gaitsgory (left) and Sam Raskin led the nine-person team that proved the geometric Langlands conjecture.

https://breakthroughprize.org/News/91
Breakthrough Prize 2025 April 5, 2025 – Los Angeles
Mathematics
Dennis Gaitsgory wins the Breakthrough Prize in Mathematics for his central role in the proof of the geometric Langlands conjecture. The Langlands program is a broad research program spanning several fields of mathematics. It grew out of a series of conjectures proposing precise connections between seemingly disparate mathematical concepts. Such connections are powerful tools; for example, the proof of Fermat’s Last Theorem reduces to a particular instance of the Langlands conjecture. These Langlands program equivalences can be thought of as generalizations of the Fourier transform, a tool that relates waves to frequency spectrums and has widespread uses from seismology to sound engineering.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1761878205/624

625: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2025/11/09(日) 16:02:39.89 ID:QrKJGO9s

つづき

In the case of the geometric Langlands conjecture, the proposed one-to-one correspondence is between two very different sets of objects, analogous to these spectrums and waves: on the spectrum side are abstract algebraic objects called representations of the fundamental group, which capture information about the kinds of loop that can wrap around certain complex surfaces; on the “wave” side are sheaves, which, loosely speaking, are rules assigning vector spaces to points on a surface. Gaitsgory has dedicated much of the last 30 years to the geometric Langlands conjecture. In 2013 he wrote an outline of the steps required for a proof, and after more than a decade of intensive research in 2024 he and his colleagues published the full proof, comprising over 800 pages spread over 5 papers. This is a monumental advance, expected to have deep implications in other areas of mathematics too, including number theory, algebraic geometry and mathematical physics.

2025 New Horizons in Mathematics Prize
Sam Raskin, Yale University
For contributions to the geometric Langlands program, including the theory of the Whittaker model and the proof of the geometric Langlands conjecture in characteristic 0.

https://people.mpim-bonn.mpg.de/gaitsgde/GLC/
Proof of the geometric Langlands conjecture
This page contains five papers, the combined content of which constitutes the proof of the (categorical, unramified) geometric Langlands conjecture.
This is a collaborative project of D. Arinkin, D. Beraldo, J. Campbell, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin and N. Rozenblyum.
Papers:
GLC I: Construction of the functor
GLC II: Kac-Moody localization and the FLE
GLC III: Compatibility with parabolic induction
GLC IV: Ambidexterity
GLC V: The multiplicity one theorem
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1761878205/625

632: １３２人目の素数さん [] 2025/11/09(日) 16:28:22.96 ID:CA6TFgJW

>>631の続き

Peter Scholze says:
April 6, 2020 at 9:28 am
I have been weighing back and forth commenting again on this matter.
However, the news in that last comment by David J. Littleboy convinced me that it might be good, even if futile, to say something again.

Peter Scholze氏は次のように述べています。
2020年4月6日午前9時28分
この件について再度コメントするかどうか、ずっと迷っていました。
しかし、David J. Littleboy氏の前回のコメントで分かったことで、たとえ無駄だとしても、もう一度発言してみるのが良いかもしれないと確信しました。

I may have not expressed this clearly enough in my manuscript with Stix, but there is just no way that anything like what Mochizuki does can work.
(I would not make this claim as strong as I am making it if I had not discussed this for with Mochizuki in Kyoto for a whole week;
the following point is extremely basic, and Mochizuki could not convince me that one dot of it is misguided, during that whole week.)
It strikes deep into my heart to think that in the name of pure mathematics, an institute could be founded for research on such questions,
and I sincerely hope that this will not come back to haunt pure mathematics.

スティックスとの原稿では十分に明確に表現できなかったかもしれませんが、望月氏のようなことは到底不可能です。
（もし京都で望月氏と丸一週間議論していなかったら、私はこれほど強く主張することはなかったでしょう。
以下の点は非常に基本的なもので、望月氏は丸一週間の間、その一つたりとも誤りだと私を納得させることはできませんでした。）
純粋数学の名の下に、このような問題を研究するための研究所が設立されるなどということは、私の心の奥底に深く突き刺さります。
そして、このことが純粋数学に再び悪影響を及ぼすことがないように心から願っています。

The reason it cannot work is a theorem of Mochizuki himself.

それがうまくいかない理由は望月氏自身の定理です。

http://rio2016.5ch.net/test/read.cgi/math/1761878205/632

636: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2025/11/09(日) 16:35:31.41 ID:QrKJGO9s

>>624-625
さて
Geometric Langlands correspondence
The claimed proof is contained in more than 1,000 pages across five papers and has been called "so complex that almost no one can explain it".
Even conveying the significance of the result to other mathematicians was described as "very hard, almost impossible" by Drinfeld.[9]
Breakthrough Prize
（Scholzeさん）
The proof represents the culmination of three decades of effort, said Peter Scholze(opens a new tab), a prominent mathematician at the Max Planck Institute for Mathematics who was not involved in the proof. “It’s wonderful to see it resolved.”
(引用終り)

1）これが、査読され雑誌掲載されたかどうかを 追跡したが
　不明だった
2）July 19, 2024のQuanta magazine から Breakthrough Prize 2025 April 5
　たったの10ヶ月間。まあ、どこかの雑誌掲載が決まっているのかもしれないが
3）にしても、Scholzeさんが ホルホルしたから Geometric Langlandsは OKで
　Scholzeさんが プッツンしたから IUTは アウトかな？
4）Scholzeさん 基準は、分かり易いよね。だが、それは 属人的だ
　数学的ではない

Geometric Langlands 1,000ページ論文を ホルホルして
IUTをアウトにする ”Scholze基準”以外の何かが あるのか？

それが なければ
ダブスタだよ　（＾＾

http://rio2016.5ch.net/test/read.cgi/math/1761878205/636

640: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2025/11/09(日) 16:53:52.93 ID:QrKJGO9s

>>635
>Dupuyも2020年頃は、望月新一のいうことにちょっとは可能性があるとおもってただろうが
>その後、望月新一から「おまえは何もわかってない」とかいう●違いな言葉を頂いて
>今では、考えを変えたかもしれない（笑）

すぐ他人を罵倒したがる 望月先生ね
まあ、数学の天才ですから・・　　；ｐ）
Dupuy先生は、March 20 to 24, 2023 と Spring 2024のアリバイは あるみたいだ　（＾＾

(参考)
https://ahgt.math.cnrs.fr/activities/workshops/AHGT-2023/
Workshop - Arithmetic & Homotopic Galois Theory 2023
March 20 to 24, 2023
List of participants
On-line attendance [46]
Taylor Dupuy University of Vermont

https://tdupu.github.io/talks.html
[ Taylor Dupuy's Homepage]
[ talks ]
Spring 2024, Inter-Universal Geometry Conference (IUGC), Tokyo Interpretations and Anabelian Geometry (slides )

https://tdupu.github.io/papers.html
[ Taylor Dupuy's Homepage]
[ Papers ]
[Preprints related to the ABC Conjecture]
Log-Kummer Correspondences and The Third Indeterminacy (with A. Hilado) --- Appendix of Interpretation Tables
The Statement of Mochizuki's Corollary 3.12, Initial Theta Data, and the First Two Indeterminacies, (with A. Hilado)
Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12, (with A. Hilado)

http://rio2016.5ch.net/test/read.cgi/math/1761878205/640

上下前次 1-新書関写板覧索設栞歴

あと 359 ﾚｽあります
ｽﾚ情報赤ﾚｽ抽出画像ﾚｽ抽出歴の未読ｽﾚ AAｻﾑﾈｲﾙ

ぬこの手ぬこTOP 0.021s