| 学部・大学院区分 | | 多・博前 | | | 時間割コード | | 3212144 | | | 科目区分 | | Ｂ類（講究）
Category B | | | 科目名 【日本語】 | | 関数解析講究４ | | | 科目名 【英語】 | | Seminar on Functional Analysis 4 | | | コースナンバリングコード | | | | | 担当教員 【日本語】 | | RICHARD Serge charles ○ | | | 担当教員 【英語】 | | RICHARD Serge charles ○ | | | 単位数 | | 4 | | | 開講期・開講時間帯 | | 秋集中 その他 その他
Intensive(Fall) Other Other | | | 授業形態 | |
| | | 学科・専攻 | | | | | 必修・選択 | | | |
| 授業の目的 【日本語】 | | Title: Spectral theory, scattering theory and C*-algebras
The aim of this seminar is to provide a broad view on functional analysis with a special emphasis on an interdisciplinary approach to spectral theory. Scattering theory, index theory for C*-algebras, non-commutative topology, and the relations between these subjects are some of the possible topics studied during this seminar. |
| | | 授業の目的 【英語】 | | | | | 到達目標 【日本語】 | | | Students will become familiar with the most recent developments of spectral theory, and get acquainted with index theorems in the context of scattering theory. |
| | | 到達目標 【英語】 | | | | | 授業の内容や構成 | | | The seminar consists in regular meetings and oral presentations made by the students. Each participant is working on a different subject and with a different support (book or articles). Everybody can benefit from the work of the other students though the presentations and the explanations provided. |
| | | 履修条件 | | | Standard undergraduate courses of calculus and functional analysis. |
| | | 関連する科目 | | The master course provided each spring semester on a topic related to this seminar, as for example "Introduction to functional analysis" (Spring 2019), "Scattering theory" (Spring 2018), "Dixmier traces" (Spring 2017), "Hilbert space methods for quantum mechanics" (Spring 2016), "K-theory for C*-algebras, and beyond" (Spring 2015), "C*-algebraic methods in spectral theory" (Spring 2014). See the link below for the corresponding lecture notes:
http://www.math.nagoya-u.ac.jp/~richard/lecture_notes.html |
| | | 成績評価の方法と基準 | | | Grade based on attendance, oral presentations and a written report. |
| | | 教科書・テキスト | | According to the interest of the students, several possible books will be proposed, as for example:
- Hilbert space methods in quantum mechanics, Amrein, 2009
- C*-algebras and operator theory, Murphy, 1990
- An introduction to K-theory for C*-algebras, Rordam, Larsen, Laustsen, 2000
- Mathematical scattering theory: general theory, Yafaev, 1991
- Basic noncommutative geometry, Khalkhali, 2010
- ... |
| | | 参考書 | | | Discussed on an individual basis. |
| | | 課外学習等（授業時間外学習の指示） | | | | | 注意事項 | | | | | 他学科聴講の可否 | | | | | 他学科聴講の条件 | | | This seminar is intended for master students from the graduate school of mathematics, but any motivated student can also attend it. |
| | | レベル | | | | | キーワード | | | Spectral and scattering theory, C*-algebras, K-theory, index theorems. |
| | | 履修の際のアドバイス | | | It is certainly easier to start expressing yourself in English in the quiet environment of a seminar rather than later on in a busy life. |
| | | 授業開講形態等 | | | | | 遠隔授業（オンデマンド型）で行う場合の追加措置 | | | |
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