授業の目的 【日本語】
Goals of the Course(JPN) | | |
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授業の目的 【英語】
Goals of the Course | | 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. |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | |
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到達目標 【英語】
Objectives of the Course | | | Students will become familiar with the most recent developments of spectral theory, and get acquainted with index theorems in the context of scattering theory. |
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授業の内容や構成
Course Content / Plan | | | 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. |
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履修条件
Course Prerequisites | | | Standard undergraduate courses of calculus and functional analysis. |
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関連する科目
Related Courses | | The master course provided each spring semester on a topic related to this seminar, as for example "K-theory for C*-algebras, and beyond" (Spring 2020 & 2015), "Introduction to functional analysis" (Spring 2019), "Scattering theory" (Spring 2018), "Dixmier traces" (Spring 2017), "Hilbert space methods for quantum mechanics" (Spring 2016), "C*-algebraic methods in spectral theory" (Spring 2022 & 2014). See the link below for the corresponding lecture notes:
http://www.math.nagoya-u.ac.jp/~richard/lecture_notes.html |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | | Grade based on attendance, oral presentations and a written report. |
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教科書・テキスト
Textbook | | 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 |
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参考書
Reference Book | | | Discussed on an individual basis. |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | | Students are expected to study independently, but support is provided whenever necessary. |
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注意事項
Notice for Students | | |
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他学科聴講の可否
Propriety of Other department student's attendance | | |
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他学科聴講の条件
Conditions of Other department student's attendance | | | This seminar is intended for master students from the graduate school of mathematics, but any motivated student can also attend it. |
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レベル
Level | | |
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キーワード
Keyword | | | Spectral and scattering theory, C*-algebras, K-theory, index theorems. |
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履修の際のアドバイス
Advice | | | 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. |
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授業開講形態等
Lecture format, etc. | | | The interactions will take place either in a classroom, my office, or on zoom, depending on the situation. |
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遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class) | | |
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