授業の目的 【日本語】
Goals of the Course(JPN) | | The general theme of this seminar is "Algebraic structures in the theory of zeta functions and automorphic forms". In particular the connection of multiple zeta values and modular forms could are possbible topic.
Depending on the student he/she could choose to work on a project which considers the
1) Theoretical aspects (Hopf algebra structures, Quasi-shuffle algebras,...),
2) Combinatorial aspects (e.g. q-analogues of multiple zeta values and partitions, Schur multiple zeta values,...),
3) Computational aspects (implementing algebraic structures in CAS),
of the seminar theme. At the beginning of the seminar, the lecturer would introduce different areas in this field.
The goal would be to work on projects which are closely related to current active research. Interested students should have a look at the references: https://www.usna.edu/Users/math/meh/biblio.html, where they can find a list of papers in the research area of this seminar. |
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授業の目的 【英語】
Goals of the Course | | The general theme of this seminar is "Algebraic structures in the theory of zeta functions and automorphic forms". In particular the connection of multiple zeta values and modular forms could are possbible topic.
Depending on the student he/she could choose to work on a project which considers the
1) Theoretical aspects (Hopf algebra structures, Quasi-shuffle algebras,...),
2) Combinatorial aspects (e.g. q-analogues of multiple zeta values and partitions, Schur multiple zeta values,...), 3) Computational aspects (implementing algebraic structures in CAS),
of the seminar theme. At the beginning of the seminar, the lecturer would introduce different areas in this field.
The goal would be to work on projects which are closely related to current active research. Interested students should have a look at the references: https://www.usna.edu/Users/math/meh/biblio.html, where they can find a list of papers in the research area of this seminar. |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | | The goal will be to give an introduction into the highly active and exciting research area of multiple zeta values and in the related algebraic structures. The students will learn to read and understand current research articles and how to come up with new questions on their own. The current plan is to also do some special meetings online about programming related to the topics in the seminar. |
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到達目標 【英語】
Objectives of the Course | | | The goal will be to give an introduction into the highly active and exciting research area of multiple zeta values and in the related algebraic structures. The students will learn to read and understand current research articles and how to come up with new questions on their own. The current plan is to also do some special meetings online about programming related to the topics in the seminar. |
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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 linear algebra and algebra or number theory. If the student wants to work on a project related to analytic and/or modular aspects knowledge of complex analysis is necessary.
If the students want to work on computational aspects it is expected that he/she has knowledge in programming and/or using CAS (e.g. pari gp, sage, mathematica, maple).
Interested students should also have a look at my lecture "Multiple zeta values and modular forms":
https://www.henrikbachmann.com/mzv2020.html
https://www.usna.edu/Users/math/meh/biblio.html |
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関連する科目
Related Courses | | There will be a graduate class in the Spring Semester 2022 on "q-analogues of multiple zeta values and finite multiple zeta values". In this small class we can discuss topics related to this lecture. Besides this there is the following lecture from Spring 2020, which contains a lot of materials & videos: "Multiple zeta values and modular forms":
https://www.henrikbachmann.com/mzv2020.html
Any lecture related to number theory and algebra. |
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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 | | |
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参考書
Reference Book | | References will be provided on an individual basis. A list of related research papers can be found here: https://www.usna.edu/Users/math/meh/biblio.html
The course of MZV & Modular forms (https://www.henrikbachmann.com/mzv2020.html) and on finite MZV and q-analaogues (https://www.henrikbachmann.com/qmzv_fmzv.html) or modular forms (https://www.henrikbachmann.com/mf_2023.html) also contains a list of references on the subject.
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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) | | | The participants of this small class are expected to give a presentation in the class. The topics will be discussed with the instructor at the beginning of the class. It is expected that the students read related research papers & lectures notes outside the course and prepare their presentation and provide handouts for the participants. We will use overleaf to work together on the handouts and every participant is expected to give comments to the handouts of the other students. |
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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. In particular students from computer science are also invited to join if they want to work on a computer science project which has a focus/connection to mathematical structures. |
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レベル
Level | | |
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キーワード
Keyword | | | Modular forms, multiple zeta values, q-series calculus, Quasi-shuffle algebras, q-analogues of multiple zeta values, Hopf algebra structures, Implementation in CAS (pari/gp, sagemath) |
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履修の際のアドバイス
Advice | | | Japanese students could use this seminar to work on a project in english. A quiet and friendly environment like this seminar could be a good place to improve the ability of doing and presenting research in english. |
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授業開講形態等
Lecture format, etc. | | | If possible this small class will be done in person, but we might switch to Zoom meetings if necessary. |
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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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