| Academic Year |
2024Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
| Lecture Code |
WSA36000 |
Subject Classification |
Specialized Education |
| Subject Name |
多様幾何特論Ｄ |
Subject Name
（Katakana） |
タヨウキカトクロンデー |
Subject Name in
English |
Topics in Geometry D |
| Instructor |
OKUDA TAKAYUKI,ISHIHARA KAI,FUJIMORI SHOICHI |
Instructor
(Katakana) |
オクダ タカユキ,イシハラ カイ,フジモリ ショウイチ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Weds5-6,Fri7-8：SCI E208 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
|
| |
| Credits |
2.0 |
Class Hours/Week |
|
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 |
lesson1 Introduction
lesson2 Coding theory on metric spaces
lesson3 Error correcting codes
lesson4 Kissing number problems
lesson5 Compact homogeneous spaces
lesson6 Inner-distributions of point arrangements on compact homogeneous spaces
lesson7 Haar measures on compact groups
lesson8 Linear representations of compact groups
lesson9 Intertwining operators
lesson10 Compact Gelfand pairs and commutative compact homogeneous spaces
lesson11 Peter--Weyl's theorem on commutative spaces.
lesson12 Spherical Fourier analysis on commutative spaces.
lesson13 An application of Spherical Fourier analysis on coding theory on commutative spaces
lesson14 For non-commutative spaces
lesson15 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. |