授業の目的【日本語】
|
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). |
授業の目的【英語】
|
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). |
到達目標【日本語】
|
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). |
到達目標【英語】
|
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. |
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 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. |
関連する科目
|
There will be a graduate class in the Spring Semester 2023 on "modular forms". In this small class we can discuss topics related to this lecture. Besides this one can find lecture notes on my previous courses on (finite) multiple zeta values on my homepage here: ![[外部サイト]](/ja/img/othersite_x2.jpg) https://www.henrikbachmann.com/teaching.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
|
See References |
参考書
|
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 |
課外学習等 (授業時間外学習の指示)
|
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. |
注意事項
|
Please contact me in advance to discuss possible topics: henrik.bachmann (at) math.nagoya-u.ac.jp |
質問への対応方法
|
|
他学科聴講の可否
|
|
他学科聴講の条件
|
|
レベル
|
2 |
キーワード
|
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) |
履修の際のアドバイス
|
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. |
授業開講形態等
|
If possible this small class will be done in person in a seminar style. |
遠隔授業(オンデマンド型)で行う場合の追加措置
|
|
2023年度 
