授業の目的 【日本語】 Goals of the Course(JPN) | | To gain a deeper understanding of one or several topics in the representation theory of algebras and/or homological algebra. The topic will depend on the interests of the participating students. |
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授業の目的 【英語】 Goals of the Course | | To gain a deeper understanding of one or several topics in the representation theory of algebras and/or homological algebra. The topic will depend on the interests of the participating students. |
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到達目標 【日本語】 Objectives of the Course(JPN)) | | At the end of the course, students should have: 1. an understanding of the main concepts and ideas in the area covered by the course; 2.capacity to apply results from the course to solve mathematical problems; 3. a thorough understanding of the concept of a mathematical proof; and 4. capacity to appy the theory to prove new results within the scope of the course. |
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到達目標 【英語】 Objectives of the Course | | At the end of the course, students should have: 1. an understanding of the main concepts and ideas in the area covered by the course; 2.capacity to apply results from the course to solve mathematical problems; 3. a thorough understanding of the concept of a mathematical proof; and 4. capacity to appy the theory to prove new results within the scope of the course. |
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授業の内容や構成 Course Content / Plan | | One or several topics in the representation theory of algebras and/or homological algebra, including: Auslander–Reiten theory; modular representation theory of finite groups; cluster-tilting theory; derived and triangulated categories. |
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履修条件 Course Prerequisites | | A good command of undergraduate algebra (groups, rings, fields) is necessary to follow this course. |
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関連する科目 Related Courses | | Courses about rings and modules, and representation theory. |
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成績評価の方法と基準 Course Evaluation Method and Criteria | | Homework assignments and/or oral presentations. |
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教科書・テキスト Textbook | | Will be decided after a discussion with the students. |
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参考書 Reference Book | | Will be introduced in the seminar. |
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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) | | Homework assignments to be completed outside of class hours. Additionally, it is recommended to revise the content of the previous lecture(s) in advance of each class. |
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注意事項 Notice for Students | | Prospective students are encouraged to contact the instructor in advance. |
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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 | | |
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レベル Level | | |
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キーワード Keyword | | Representation theory of algebras, Auslander–Reiten theory, cluster-tilting theory, homological algebra, derived categories, triangulated categories. |
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履修の際のアドバイス Advice | | Do not be afraid to ask questions! |
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授業開講形態等 Lecture format, etc. | | Discussions with the instructor (individual or in groups) and oral presentations by the students and/or the instructor. The classes will be held online or in a classroom, depending on the preferences of the participants. |
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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) | | It will be possible to follow the course online. If you wish to do so, please contact the instructor before the start of the course. |
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