日本語 English
| 開講年度/ Academic YearAcademic Year |
20262026 |
| 科目設置学部/ CollegeCollege |
理学研究科/Graduate School of ScienceGraduate School of Science |
| 科目コード等/ Course CodeCourse Code |
LC144/LC144LC144 |
| テーマ・サブタイトル等/ Theme・SubtitleTheme・Subtitle |
非線型微分方程式の組合せ論 |
| 授業形態/ Class FormatClass Format |
対面（全回対面）/Face to face (all classes are face-to-face)Face to face (all classes are face-to-face) |
| 授業形態（補足事項）/ Class Format (Supplementary Items)Class Format (Supplementary Items) |
|
| 授業形式/ Class StyleCampus |
講義/LectureLecture |
| 校地/ CampusCampus |
池袋/IkebukuroIkebukuro |
| 学期/ SemesterSemester |
秋学期/Fall semesterFall semester |
| 曜日時限・教室/ DayPeriod・RoomDayPeriod・Room |
水5/Wed.5 Wed.5 ログインして教室を表示する（Log in to view the classrooms.） |
| 単位/ CreditsCredits |
22 |
| 科目ナンバリング/ Course NumberCourse Number |
MAT6390 |
| 使用言語/ LanguageLanguage |
日本語/JapaneseJapanese |
| 履修登録方法/ Class Registration MethodClass Registration Method |
科目コード登録/Course Code RegistrationCourse Code Registration |
| 配当年次/ Assigned YearAssigned Year |
配当年次は開講学部のR Guideに掲載している科目表で確認してください。配当年次は開講学部のR Guideに掲載している科目表で確認してください。 |
| 先修規定/ Prerequisite RegulationsPrerequisite Regulations |
|
| 他学部履修可否/ Acceptance of Other CollegesAcceptance of Other Colleges |
履修登録システムの『他学部・他研究科履修不許可科目一覧』で確認してください。 |
| 履修中止可否/ Course CancellationCourse Cancellation |
－（履修中止制度なし/ No system for cancellation) |
| オンライン授業60単位制限対象科目/ Online Classes Subject to 60-Credit Upper LimitOnline Classes Subject to 60-Credit Upper Limit |
|
| 学位授与方針との関連/ Relationship with Degree PolicyRelationship with Degree Policy |
各授業科目は、学部・研究科の定める学位授与方針（DP）や教育課程編成の方針（CP）に基づき、カリキュラム上に配置されています。詳細はカリキュラム・マップで確認することができます。 https://www.rikkyo.ac.jp/about/disclosure/educational_policy/science.html |
| 備考/ NotesNotes |
CA208解析学諸論6、RC144解析学特論6と合同授業 |
I will talk about an elementary part of the Sato theory on integrable systems, i.e., KP theory, restricting to the finite dimensional sector.
More than 40 years have passed since Mikio Sato announced his theory on KP hierarchy. Several good references exist now. However I would like to give a series of lectures of the subject in the original naive form which I learned from Sato himself.
KP theory is algebraic analysis on an infinite dimensional Grassmann manifold and
there is difficulty caused by infinite dimensions. In this series, I restrict myself to the finite dimensional case and discuss some combinatorics inherent in the theory.
| 1 | Historical introduction of solitons and classical integrable systems |
| 2 | Ordinary differential operators and Grassmann manifolds |
| 3 | Time evolutions as dynamical systems on the Grassmann manifold |
| 4 | Tau functions |
| 5 | Schur functions and some other symmetric functions |
| 6 | Lax formalism and Sato formalism |
| 7 | Projective embedding of the Grassmann manifold |
| 8 | Hirota's direct method for soliton solutions |
| 9 | Addition formula of tau functions |
| 10 | KdV hierarchy and modified KdV hierarchy |
| 11 | Gelfand-Dickey-Sato basis |
| 12 | Fock representation of the Virasoro algebra |
| 13 | Virasoro algebra and KP hierarchy |
| 14 | Prospect |
板書 /Writing on the Board
スライド（パワーポイント等）の使用 /Slides (PowerPoint, etc.)
上記以外の視聴覚教材の使用 /Audiovisual Materials Other than Those Listed Above
個人発表 /Individual Presentations
グループ発表 /Group Presentations
ディスカッション・ディベート /Discussion/Debate
実技・実習・実験 /Practicum/Experiments/Practical Training
学内の教室外施設の利用 /Use of On-Campus Facilities Outside the Classroom
校外実習・フィールドワーク /Field Work
上記いずれも用いない予定 /None of the above
代数学（群論，環論，加群論，．．．）をしっかり復習しておくと理解が深まると思う．
| 種類 (Kind) | 割合 (%) | 基準 (Criteria) |
|---|---|---|
| 平常点 (In-class Points) | 100 |
授業内レポート（複数回）(100%) |
| 備考 (Notes) | ||
なし/None
| No | 著者名 (Author/Editor) | 書籍名 (Title) | 出版社 (Publisher) | 出版年 (Date) | ISBN/ISSN |
|---|---|---|---|---|---|
| 1 | 山田裕史 | 『組合せ論プロムナード（増補版）』 | 日本評論社 | 2024 | 9784535790179 |
| 2 | 山田裕史 | 『組合せ論トレイル』 | 日本評論社 | 2024 | 9784535790186 |
佐藤幹夫らにより展開された可積分系の理論（KP理論）の易しい部分，すなわち有限次元グラスマン多様体に制限したあたりをお話ししたい．
I will talk about an elementary part of the Sato theory on integrable systems, i.e., KP theory, restricting to the finite dimensional sector.
佐藤理論が発表されて40余年，随分と整理されて文献も増えてきたような気もするが，佐藤幹夫の講義を直に聴いた世代の一人として，ごく初期の素朴な形で残しておきたいと考える．KP理論は無限次元グラスマン多様体の話であり，本質的に無限次元特有の難しさがあるが，ここではトイモデルとして組合せ論的な記述が易しい有限次元のヴァージョンに限定したい．
More than 40 years have passed since Mikio Sato announced his theory on KP hierarchy. Several good references exist now. However I would like to give a series of lectures of the subject in the original naive form which I learned from Sato himself.
KP theory is algebraic analysis on an infinite dimensional Grassmann manifold and
there is difficulty caused by infinite dimensions. In this series, I restrict myself to the finite dimensional case and discuss some combinatorics inherent in the theory.
| 1 | Historical introduction of solitons and classical integrable systems |
| 2 | Ordinary differential operators and Grassmann manifolds |
| 3 | Time evolutions as dynamical systems on the Grassmann manifold |
| 4 | Tau functions |
| 5 | Schur functions and some other symmetric functions |
| 6 | Lax formalism and Sato formalism |
| 7 | Projective embedding of the Grassmann manifold |
| 8 | Hirota's direct method for soliton solutions |
| 9 | Addition formula of tau functions |
| 10 | KdV hierarchy and modified KdV hierarchy |
| 11 | Gelfand-Dickey-Sato basis |
| 12 | Fock representation of the Virasoro algebra |
| 13 | Virasoro algebra and KP hierarchy |
| 14 | Prospect |
板書 /Writing on the Board
スライド（パワーポイント等）の使用 /Slides (PowerPoint, etc.)
上記以外の視聴覚教材の使用 /Audiovisual Materials Other than Those Listed Above
個人発表 /Individual Presentations
グループ発表 /Group Presentations
ディスカッション・ディベート /Discussion/Debate
実技・実習・実験 /Practicum/Experiments/Practical Training
学内の教室外施設の利用 /Use of On-Campus Facilities Outside the Classroom
校外実習・フィールドワーク /Field Work
上記いずれも用いない予定 /None of the above
代数学（群論，環論，加群論，．．．）をしっかり復習しておくと理解が深まると思う．
| 種類 (Kind) | 割合 (%) | 基準 (Criteria) |
|---|---|---|
| 平常点 (In-class Points) | 100 |
授業内レポート（複数回）(100%) |
| 備考 (Notes) | ||
なし/None
| No | 著者名 (Author/Editor) | 書籍名 (Title) | 出版社 (Publisher) | 出版年 (Date) | ISBN/ISSN |
|---|---|---|---|---|---|
| 1 | 山田裕史 | 『組合せ論プロムナード（増補版）』 | 日本評論社 | 2024 | 9784535790179 |
| 2 | 山田裕史 | 『組合せ論トレイル』 | 日本評論社 | 2024 | 9784535790186 |