Hiroshima University Syllabus

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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
Subject Name in
Topics in Geometry D
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:Online
Lesson Style Lecture Lesson Style
(More Details)
Credits 2.0 Class Hours/Week   Language of Instruction B : Japanese/English
Course Level 4 : Undergraduate Advanced
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
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(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.  
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
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Learning techniques to be incorporated  
Suggestions on
Preparation and
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.  
Grading Method Evaluation will be based on homework assignments.   
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
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. 
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