学部・大学院区分
Undergraduate / Graduate
多・博前
時間割コード
Registration Code
3212186
科目区分
Course Category
B類(講究)
Category B
科目名 【日本語】
Course Title
整数論講究2
科目名 【英語】
Course Title
Seminar on Number Theory 2
コースナンバリングコード
Course Numbering Code
担当教員 【日本語】
Instructor
BACHMANN Henrik lennart ○
担当教員 【英語】
Instructor
BACHMANN Henrik lennart ○
単位数
Credits
4
開講期・開講時間帯
Term / Day / Period
秋集中 その他 その他
Intensive(Fall) Other Other
授業形態
Course style

学科・専攻
Department / Program
多元数理科学研究科
必修・選択
Required / Selected


授業の目的 【日本語】
Goals of the Course(JPN)
The general theme of this seminar would be "Algebraic structures in the theory of zeta functions and automorphic forms". In particular the connection of multiple zeta values and modular forms could be one 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.
授業の目的 【英語】
Goals of the Course
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.
到達目標 【英語】
Objectives of the Course
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.
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
関連する科目
Related Courses
"Multiple zeta values and modular forms":
https://www.henrikbachmann.com/mzv2020.html

Any lecture related to number theory and algebra.
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.
教科書・テキスト
Textbook
See references
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) also contains a list of references on the subject.
課外学習等(授業時間外学習の指示)
Study Load(Self-directed Learning Outside Course Hours)
注意事項
Notice for Students
-
他学科聴講の可否
Propriety of Other department student's attendance
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.
レベル
Level
3
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
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.
授業開講形態等
Lecture format, etc.
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)