| Academic Year |
2025Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
| Lecture Code |
WSA35000 |
Subject Classification |
Specialized Education |
| Subject Name |
多様幾何特論Ｃ |
Subject Name
（Katakana） |
タヨウキカトクロンシー |
Subject Name in
English |
Topics in Geometry C |
| Instructor |
OKUDA TAKAYUKI,FUJIMORI SHOICHI |
Instructor
(Katakana) |
オクダ タカユキ,フジモリ ショウイチ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, First Semester, 2Term |
| Days, Periods, and Classrooms |
(2T) Mon7-8,Weds7-8：SCI E208 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
B
:
Japanese／English |
| Course Level |
7
:
Graduate Special Studies
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Homogeneous spaces, Coding theory, Representation theory, Fourier analysis |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Class Objectives
/Class Outline |
The purpose is to understand applications of Fourier analysis on coding theory on homogeneous spaces. |
| Class Schedule |
Lesson 1: Introduction
Lesson 2: Tensor products of vector spaces
Lesson 3: Involutive algebras
Lesson 4: Representation theory on finite groups
Lesson 5: Harmonic analysis on finite homogeneous spaces
Lesson 6: Fourier transforms on commutative finite homogeneous spaces
Lesson 7: Distance regular graphs
Lesson 8: Association schemes
Lesson 9: Bose--Mesner algebras
Lesson 10: Fourier transforms on commutative association schemes
Lesson 11: Matrix algebras on probability spaces
Lesson 12: Compact homogeneous spaces
Lesson 13: Compact association schemes II
Lesson 14: Compact association schemes II
Lesson 15: Summary
Homework will be assigned in the lecture. |
Text/Reference
Books,etc. |
No textbook.
Reference books:
Bannai, E., Bannai, E., Ito, T., & Tanaka, R. (2021). Algebraic combinatorics (Vol. 5). Walter de Gruyter GmbH & Co KG.
Toshiyuki Kobayashi (小林俊行), Toshio Oshima (大島利雄), Lie group and Representation theory (in Japanese: リー群と表現論), Iwanami, 2005 |
PC or AV used in
Class,etc. |
|
| (More Details) |
|
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
In each lecture, some easy computations and proofs will be omitted.
It is needed to check them by your hand.
Asking questions to the lecturer is always welcome. |
| Requirements |
|
| Grading Method |
Evaluation will be based on homework assignments. |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |