ガロア第一論文と乗数イデアル他関連資料スレ11

[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ11 (1002ﾚｽ)
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832: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2024/12/29(日) 08:56:12.75 ID:aRTKq65A

>>824-82 追加
>緒方芳子さんで，その業績に対してごく最近猿橋賞が授与されたのは記憶にあたらしい．緒方さんがポアンカレ賞を受賞なさったときの記事も『数学通信』の第26巻第4号にある

立川　裕二氏の記事は、下記「数学通信」第２９巻第３号 ２０２４年　１１月 Ｐ43
緒方芳子さん 猿橋賞の記事も同じ号にある
「数学通信」第２６巻第4号も貼っておきます

www.mathsoc.jp/publications/tushin/backnumber/index29-3.html
「数学通信」第２９巻第３号目次　２０２４年　１１月
・山下真由子さんの令和6年度科学技術分野の文部科学大臣表彰若手科学者賞受賞に寄せて 立川　裕二 ４３
・www.mathsoc.jp/assets/file/publications/tushin/2903/ogata-tasaki.pdf
　緒方芳子さんの猿橋賞および令和6年度科学技術分野の文部科学大臣表彰科学技術賞受賞に寄せて 田崎　晴明 ２０
　
www.mathsoc.jp/publications/tushin/backnumber/index26-4.html
「数学通信」第２６巻第4号目次
・www.mathsoc.jp/assets/file/publications/tushin/2604/ogata-kawahigashi.pdf
　緒方芳子氏の Henri Poincaré Prize 受賞に寄せて 河東　泰之 ２９
ついでに
・www.mathsoc.jp/assets/file/publications/tushin/2604/mori-mukai.pdf
　森重文氏の文化勲章受章に寄せて―温故而知新，可以為師矣 向井　　茂 ２２
・www.mathsoc.jp/assets/file/publications/tushin/2604/mochizuki-kawaguchi.pdf
　望月拓郎さんの Breakthrough Prize 受賞に寄せて 川口　　周 ３５

http://rio2016.5ch.net/test/read.cgi/math/1724969804/832

843: １３２人目の素数さん [] 2024/12/29(日) 22:05:32.84 ID:aRTKq65A

>>841-842
>Q.　Exotic R^4には、通常のC^2とは異なる複素構造が入る？
>それは未解決だと思う

それは、ずいぶん面白い問いだと思う
まず、Exotic R4とは？
SmallとLargeがあるらしい

そのまえに、通常のC^2には、通常のR^4と微分同相か？ という問いがあるだろう。多分Yesかな
とすると、C^2にも Exoticな（通常と非微分同相な）微分可能構造が入るか？ という問題設定かな？ 多分Yesかな

Cをリーマン球に丸めて、C'と書く。C'^2 はどうか？ 頭が働かない・・ ；ｐ）
ところで、exotic 4-sphereについて
”a counterexample to the smooth generalized Poincaré conjecture in dimension 4. Some plausible candidates are given by Gluck twists.”
とあるね

(参考)
en.wikipedia.org/wiki/Exotic_R4
Exotic R4

Small exotic R4s

Large exotic R4s
Michael Hartley Freedman and Laurence R. Taylor (1986) showed that there is a maximal exotic
R4, into which all other
R4 can be smoothly embedded as open subsets.

Related exotic structures
Casson handles are homeomorphic to
D2×R2 by Freedman's theorem (where
D2 is the closed unit disc) but it follows from Donaldson's theorem that they are not all diffeomorphic to
D2×R2.
In other words, some Casson handles are exotic
D2×R2.

It is not known (as of 2024) whether or not there are any exotic 4-spheres; such an exotic 4-sphere would be a counterexample to the smooth generalized Poincaré conjecture in dimension 4. Some plausible candidates are given by Gluck twists.

en.wikipedia.org/wiki/Exotic_sphere#4-dimensional_exotic_spheres_and_Gluck_twists
4-dimensional exotic spheres and Gluck twists
In 4 dimensions it is not known whether there are any exotic smooth structures on the 4-sphere. The statement that they do not exist is known as the "smooth Poincaré conjecture", and is discussed by Michael Freedman, Robert Gompf, and Scott Morrison et al. (2010) who say that it is believed to be false.

Some candidates proposed for exotic 4-spheres are the Cappell–Shaneson spheres (Sylvain Cappell and Julius Shaneson (1976)) and those derived by Gluck twists (Gluck 1962). Gluck twist spheres are constructed by cutting out a tubular neighborhood of a 2-sphere S in S4 and gluing it back in using a diffeomorphism of its boundary S2×S1. The result is always homeomorphic to S4. Many cases over the years were ruled out as possible counterexamples to the smooth 4 dimensional Poincaré conjecture. For example, Cameron Gordon (1976), José Montesinos (1983), Steven P. Plotnick (1984), Gompf (1991), Habiro, Marumoto & Yamada (2000), Selman Akbulut (2010), Gompf (2010), Kim & Yamada (2017).

ja.wikipedia.org/wiki/%E3%82%A8%E3%82%AD%E3%82%BE%E3%83%81%E3%83%83%E3%82%AF_R4
エキゾチック R4

http://rio2016.5ch.net/test/read.cgi/math/1724969804/843

845: １３２人目の素数さん [] 2024/12/29(日) 23:32:55.51 ID:aRTKq65A

"Exotic R4 and quantum field theory"か
”the spinor Φ as solution of the Dirac equation (18)”と関係しているのか？

https://iopscience.iop.org/article/10.1088/1742-6596/343/1/012011/pdf
7th International Conference on Quantum Theory and Symmetries (QTS7)
Journal of Physics: Conference Series 343 (2012) 012011
Exotic R4 and quantum field theory Torsten Asselmeyer-Maluga and Roland Mader German Aerospace center, Rutherfordstr. 2, 12489 Berlin, Germany

P14
As conclusion we can state that an immersed disk used in the construction of exotic R4 are described by a parallel spinor Φ.
The correspondence goes further because the spinor Φ as solution of the Dirac equation (18) is not only generated by a propagator but also by the immersed disk itself.
The Feynman path integral of this action can be rearranged by a simply reorganization of the perturbative series in terms of trees [65].
It should be especially emphasized that this method do not need any discretization of the phase space or cluster expansion.
Then we obtain a close relation between trees and renormalization similar to approach of Connes and Kreimer [66].
We close this paper with these conjectural remarks.

http://rio2016.5ch.net/test/read.cgi/math/1724969804/845

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