授業の目的 【日本語】
Goals of the Course(JPN) | | Title 1: 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.
Title 2: Graphs and epidemiology
The aim of this seminar is to study the evolution of epidemics on graphs, with an emphasize on dynamic graphs. |
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授業の目的 【英語】
Goals of the Course | | |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | | For the first subject, students will become familiar with the most recent developments of spectral theory, and get acquainted with index theorems in the context of scattering theory. For the second subject, students will study the very recent investigations on this hot topic. |
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到達目標 【英語】
Objectives of the Course | | |
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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. For the second subject, any course on stochastic processes or on graph theory would be an asset |
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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 2014). See the link below for the corresponding lecture notes:
http://www.math.nagoya-u.ac.jp/~richard/lecture_notes.html
A master course on graphs and epidemiology will be presented in Spring 2021. |
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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
- Networks, Newman, 2018
- Mathematics of epidemics on networks, Kiss, Miller, Simon, 2017 |
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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) | | |
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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 | | 1) Spectral and scattering theory, C*-algebras, K-theory, index theorems.
2) Graphs and random graphs, SIR and SIS models, epidemiology. |
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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. | | |
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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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