そこから 下記へ行ける https://direct.mit.edu/books/oa-monograph/5460/Sheaf-Theory-through-Examples Sheaf Theory through ExamplesOpen Access By Daniel Rosiak The MIT Press DOI: https://doi.org/10.7551/mitpress/12581.001.0001 ISBN electronic: 9780262370424 Publication date: 2022
ここに、Book PDF というリンクアイコンがあって（リンクは貼らないので自分で訪問すること） そこから、PDF図書が落とせる
Grokさん偉いね Grokさんと、一つ対局してみるかな？ｗ ；ｐ） ＜目次＞ 1 Categories 21 1.1 Categorical Preliminaries 21 1.2 A Few More Examples 35 1.3 Returning to the Definition and Distinctions of Size 36 1.4 Some New Categories from Old 40 1.5 Aside on “No Objects” 43
2 Prelude to Sheaves: Presheaves 45 2.1 Functors 46 2.2 Natural Transformations 61 2.3 Seeing Structures as Presheaves 65 2.4 The Presheaf Action 71 2.5 Philosophical Pass: The Four Action Perspectives 85
3 Universal Constructions 89 3.1 Limits and Colimits 89 3.2 Philosophical Pass: Universality and Mediation 104
4 Topology: A First Pass at Space 109 4.1 Motivation 109 4.2 A Dialogue Introducing the Key Notions of Topology 111 4.3 Topology and Topological Spaces More Formally 123 4.4 Philosophical Pass: Open Questions 144
5 First Look at Sheaves 147 5.1 Sheaves: The Topological Definition 147 5.2 Examples 151 5.3 Philosophical Pass: Sheaf as Local-Global Passage 168
6 There’s a Yoneda Lemma for That 171 6.1 First, Enrichment! 171 6.2 Downsets and Yoneda in the Miniature 175 6.3 Representability Simplified 179 6.4 More on Representability, Fixed Points, and a Paradox 183 以下略
>>470 追加 Sheaf Theory through ExamplesOpen Access Daniel Rosiak
Introduction Open Access https://direct.mit.edu/books/oa-monograph/chapter-pdf/2368031/c000400_9780262370424.pdf
P11より This system of mutually compatible local data assignments or “measurements” of the happenings on the space—where the various data assignments are, piece by piece, constrained by one another, and thereby patched together to supply an assignment over the entire space covered by the individual regions—is, in essence, what constitutes our sheaf. The idea is that the data assignments are being “tied together” in a natural way
where this last picture is meant to serve as motivation or clarification regarding the agricultural terminology of “sheaf”:
Here one thinks of various regions as the parcels of an overall space covered by those pieces, the collection of which then serves as a site where certain happenings are held to take place, and the abstract sensors capturing local snapshots or measurements of all that is going on in each parcel are then regarded as being collected together into “stalks” of data, regarded as sitting over (or growing out of) the various parts of the ground space
506 名前：to which they are attached. A selection of a particular snapshot made from each of the individual stalks (collections of snapshots) amounts to a cross-section and the process of restriction (along intersecting regions) and collation (along unions of regions) of these sections captures how the various stalks of data are bound together. (引用終り)
(参考) https://ja.wikipedia.org/wiki/%E6%9D%9F_(%E6%9D%9F%E8%AB%96) 束 (束論) 出典 1^ Dedekind, Richard (1897), “Ueber Zerlegungen von Zahlen durch ihre grössten gemeinsamen Teiler”, Braunschweiger Festschrift: 1–40
https://de.wikipedia.org/wiki/Verband_(Mathematik) Verband (Mathematik) google英訳 Association (mathematics) In mathematics, a lattice is a structure that can be completely described as both an order structure and an algebraic structure . Hasse diagrams for some examples → Main article : Hasse diagram
https://context.reverso.net/%E7%BF%BB%E8%A8%B3/%E3%83%89%E3%82%A4%E3%83%84%E8%AA%9E-%E6%97%A5%E6%9C%AC%E8%AA%9E/Verband?d=0 reverso.net 独語辞書 der Verbandnm Ich hab 'n Verband gefunden. なぜか包帯が巻かれてた Warum nimmst du den Verband nicht ab? 彼の包帯を取ってみたらいい？ Der Verband bietet Verbrauchern und Kunden Rückgriff auf rohe Nachlassforschungsunternehmen. この協会は、消費者および顧客に不正な検定調査会社に対する訴求を提供する。
https://fr.wikipedia.org/wiki/Treillis_(ensemble_ordonn%C3%A9) Treillis (ensemble ordonné) ( google訳：格子（順序集合）) En mathématiques, un treillis[1] (en anglais : lattice) est une des structures algébriques utilisées en algèbre générale. Notes et références [1]N. Bourbaki, Éléments de mathématique : Théorie des ensembles [détail des éditions], p. ER.28, aperçu sur Google Livres, parle d'« ensemble réticulé, ou réseau ordonné (ou lattis) ».
>S先生はバスの入り口で >「入口」を見て >What is this lambda Laplacian? >と尋ねられた。
Copilot に入れてみると Q: What is this lambda Laplacian? A: The Laplacian is a differential operator that plays a crucial role in mathematics and physics, particularly in areas like potential theory, differential equations, and quantum mechanics. It is often denoted as Δ or ∇² and is defined as the sum of second partial derivatives: [ \Delta f = \frac{\partial2} + \frac{\partial2} + \frac{\partial2} ] If you're referring to a lambda Laplacian, it could relate to eigenvalues of the Laplacian operator in spectral theory. The eigenvalue problem for the Laplacian is: [ \Delta f = \lambda f ] where λ represents an eigenvalue associated with the Laplacian. This arises in various contexts, such as solving the Helmholtz equation, studying heat diffusion, and analyzing vibrational modes. Would you like to explore its applications in functional analysis or spectral geometry? (引用終り)
なので、”λ represents an eigenvalue associated with the Laplacian”と 固有値の連想ゲームです バスの入り口に、Δ or ∇ が有ったのでしょうか？ （＾＾
(参考) https://en.wikipedia.org/wiki/DBAR_problem DBAR problem The DBAR problem is of key importance in the theory of integrable systems, Schrödinger operators and generalizes the Riemann–Hilbert problem.[1][2][3]
References [2]Haslinger, Friedrich (2014). The d-bar Neumann Problem and Schrödinger Operators. Walter de Gruyter GmbH & Co KG. ISBN 978-3-11-031535-6. PDF https://www.mat.univie.ac.at/~has/dbar/dbar1.pdf Preface The rst chapters contain a discussion of Bergman spaces and of the solution operator to @ restricted to holomorphic L2 -functions in one complex variable, pointing out that the Bergman kernel of the associated Hilbert space of holomorphic functions plays an important role.
The next chapter contains a detailed account of the application of the @-methods to Schr odinger operators, Pauli and Dirac operators and to Witten-Laplacians.
In this way one obtains a rather general basic estimate, from which one gets H ormander's L2 -estimates for the solution of the CauchyRiemann equation together with results on related weighted spaces of entire functions, such as that these spaces are in nite-dimensional if the eigenvalues of the Levi-matrix of the weight function show a certain behavior at in nity. In addition, it is pointed out that some L2 -estimates for @ can be interpreted in the sense of a general Brascamp-Lieb inequality.
Contents Preface iii 1. Bergman spaces 2 2. The canonical solution operator to @ restricted to spaces of holomorphic functions 10 3. Spectral properties of the canonical solution operator to @ 21 4. The @-complex 33 5. The weighted @-complex 50 6. The twisted @-complex 58 7. Applications 62 8. Schr odinger operators 69 9. Compactness 74 10. The @-Neumann operator and commutators of the Bergman projection and multiplication operators. 85
https://www.mat.univie.ac.at/~has/ Friedrich Haslinger Faculty of Mathematics University of Vienna Research interests d-bar Neumann problem Hardy and Bergman spaces in several complex variables Bergman and Szegö kernels Spectral analysis of Schrödinger operators
Liebさん In 2022 the Carl Friedrich Gauss Prize at the International Congress of Mathematicians In 2023 Lieb received Kyoto Prize in Basic Sciences for his achievements in many-body physics.[23]
https://en.wikipedia.org/wiki/Elliott_H._Lieb Elliott Hershel Lieb (born July 31, 1932) is an American mathematical physicist. He is a professor of mathematics and physics at Princeton University. Lieb's works pertain to quantum and class
532 名前：ical many-body problem,[1][2][3] atomic structure,[3] the stability of matter,[3] functional inequalities,[4] the theory of magnetism,[2] and the Hubbard model.[2] Awards In 2022 the Carl Friedrich Gauss Prize at the International Congress of Mathematicians ″for deep mathematical contributions of exceptional breadth which have shaped the fields of quantum mechanics, statistical mechanics, computational chemistry, and quantum information theory.″[16] In 2023 Lieb received Kyoto Prize in Basic Sciences for his achievements in many-body physics.[23] []
下記ですね ”Dedicated to the 100th anniversary of the creation of the Bergman kernel ”か ”Haslinger”さん 二人います Professor Fritz Haslinger さんと Friedrich Haslinger (Universität Wien) さんと 同一人物か あるいは ご親戚か？
(参考) https://sites.google.com/view/hayama-scv/2022 HAYAMA Symposium on Complex Analysis in Several Variables XXIII Dedicated to the 100th anniversary of the creation of the Bergman kernel July 23(Sat) – July 26(Tue), 2022 uly 27 and 28(Wed and Thu), 2022
Stefan Bergman publised his first paper on the reproducing kernel in 1922, which was his doctoral dissertation under the supervision of v. Mises and Erh. Schmidt. On the occasion of 100th anniversary, we plan to review recent progresses of the Bergman kernel and related topics. The meeting will be held on site but includes some online talks.
https://lh6.googleusercontent.com/BI_CyAfBu2DJC--g1CaNGsDe9pBVVbznfV47wICATIagy74a-ldg1yGaruXIxE4gjLo0l8-2UgGtflP4y__XQN4XBR-aLr0mLVIthqLiCENSVdAi01wwgHG54Cz6zSpZK-VGDe5RBZSh9dRYaGkN2gw8P5gC5uAWNAoTh2OsD3lHWV2N2_qGQw=w1280 A birthday cake made in Vienna by courtesy of Professor Fritz Haslinger.
Ph.D. Eberhard-Karls-Universität Tübingen 1953 Germany Dissertation: Several Complex Variables and Manifolds for the Cartan Conjecture Advisor: Hellmuth Kneser
(参考) https://en.wikipedia.org/wiki/Karl_Stein_(mathematician) Karl Stein (1 January 1913 in Hamm, Westphalia – 19 October 2000) was a German mathematician. He is well known for complex analysis and cryptography. Stein manifolds and Stein factorization are named after him.
google検索 K. Stein 多変数関数論 AI による概要 （AI の回答には間違いが含まれている場合があります。） K. Steinは、多変数複素関数論の重要な人物であり、特に岡潔の多変数関数論の理論に強い影響を与えました。Steinは、岡潔の理論をさらに発展させ、多変数の解析関数の性質を詳しく調べました。
Wilhelm F. Stoll 先生貼っておきます 下記”Contributions to Several Complex Variables: In Honour of Wilhelm Stoll (Aspects of Mathematics) 1986th Edition ” というのがあるのは、びつくり です （＾＾
(参考) https://www.mathｇｅｂｅａｌｏｇｙ.org/ URLが通らないので略す MathSciNet Ph.D. Eberhard-Karls-Universität Tübingen 1953 Germany Dissertation: Several Complex Variables and Manifolds for the Cartan Conjecture Advisor: Hellmuth Kneser Students: Click here to see the students listed in chronological order. 略す
google: Wilhelm F. Stoll math Several Complex Variables AI による概要:AI responses may include mistakes. Learn more Wilhelm F. Stoll was a prominent mathematician who made significant contributions to the field of several complex variables. He specialized in holomorphic functions, value distribution theory, and related topics, particularly within the context of analytic geometry and the study of complex manifolds. His work influenced many others in the field, and he is known for his dedication to mathematical research and his mentorship of doctoral students. Key Contributions and Focus Areas: Holomorphic Functions: Stoll's research focused on the properties and behavior of holomorphic functions of multiple complex variables. He explored topics like finite order holomorphic functions and their growth estimates.
Value Distribution Theory: He made valuable contributions to the theory of value distribution, which deals with how functions of multiple complex variables take on specific values. Analytic Geometry and Complex Manifolds: Stoll's work extended to the study of analytic spaces and manifolds in several complex variables, including deformation theory and the properties of pseudo-convexity. Relationship to Partial Differential Equations: He investigated the connections between complex analysis and partial differential equations, particularly in relation to analytic varieties and currents.
Influence and Legacy: Mentorship: Stoll supervised eighteen doctoral students and had a significant influence on the careers of many mathematicians. Research Articles and Publications: He published over sixty research articles and contributed to several conferences and volumes, including "Contributions to Several Complex Variables: In Honour of
<アマゾンサイトより>書籍 Contributions to Several Complex Variables: In Honour of Wilhelm Stoll (Aspects of Mathematics) 1986th Edition by Alan Howard (Editor), Pit-Mann Wong (Editor) パブリッシャー : Vieweg+Teubner Verlag （google訳） 1960年、ヴィルヘルム・ストールはノートルダム大学に数学教授として着任し、1984年10月、大学は長年の功績をたたえ、彼に敬意を表して複素解析の会議を開催しました。本書は、その会議の議事録です。ナンシー・K・スタントンと共に、会議の主催者を務めることができたのは光栄でした。ノートルダム大学理学部および米国科学財団の支援に感謝いたします。ヴィルヘルム・ストールは、60本を超える研究論文の発表と18名の博士課程学生の指導という経歴の中で、その勤勉さ、誠実さ、そして人間性により同僚の愛情と尊敬を勝ち得てきました。彼のアイデアと洞察力、そしてそれらがきっかけとなったその後の研究の影響は、本書に収録されているいくつかの論文によって証明されています。会議参加者および本書の寄稿者を代表し、ヴィルヘルム・ストール氏の数学への多年にわたる幸福な献身的な貢献を心よりお祈り申し上げます。アラン・ハワード、ピットマン・ウォン VII III ~ c: ... ~ c: o U CI> .r. ~ .... oe ::J ~ oa:: a. ::J o ... (.!:J VIII '" Q) g> a. '" Q) E z '" ..... o Q) EQ) ..c eX IX 集合写真の参加者 Qi-keng LU、中国科学院教授、北京、中国。 (引用終り) 以上
https://rio2016.5ch.net/test/read.cgi/math/1731752734/407 407１３２人目の素数さん 2025/06/09(月) 08:26:40.27ID:VL477SYt News from the AMS Fukaya Wins 2025 Shaw Prize in Mathematical Sciences May 27, 2025 https://www.ams.org/news?news_id=7494
https://www.excite.co.jp/news/article/Kyodo_prw_202505289638/ 2025年のShaw受賞者の発表 共同通信PRワイヤー 2025年05月28日(水) Shaw賞（数学科学部門）の受賞者は以下のとおりです。 深谷賢治氏 Beijing Institute of Mathematical Sciences and ApplicationsおよびTsinghua University Yau Mathematical Sciences Center教授（中華人民共和国） 授賞理由は、シンプレクティック幾何学における先駆的な業績、特に現在「深谷圏」として知られる、シンプレクティック多様体上のラグランジュ部分多様体からなる圏の存在を構想し、それを構築するという壮大な課題に主導的に取り組むとともに、シンプレクティック・トポロジー、ミラー対称性、ゲージ理論における以降の革新的かつ多大な影響を与える貢献に対してです。
https://ja.wikipedia.org/wiki/%E3%83%9B%E3%83%A2%E3%83%AD%E3%82%B8%E3%82%AB%E3%83%AB%E3%83%9F%E3%83%A9%E3%83%BC%E5%AF%BE%E7%A7%B0%E6%80%A7%E4%BA%88%E6%83%B3 ホモロジカルミラー対称性予想 歴史 1994年のチューリッヒでの国際数学者会議の報告で、コンツェビッチは次のような予想をした。 カラビ・ヤウ多様体のペア X と Y のミラー対称性は、代数多様体 X から構成された三角圏（英語版） (X 上の連接層の導来圏)と、もう一つの Y のシンプレクティック多様体から構成される三角圏(深谷圏（英語版）)の同値性として説明されるのではないか。
