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 WSA33000 Subject Classification Specialized Education
Subject Name 多様幾何特論A
Subject Name
Subject Name in
Topics in Geometry A
フジモリ ショウイチ,オクダ タカユキ
Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  2Term
Days, Periods, and Classrooms (2T) Mon3-4,Thur3-4:SCI E208
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, Proper actions, Discontinuous groups, Coarse geometry 
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 relationships between discontinuous groups on homogeneous spaces and Coarse geometry. 
Class Schedule lesson1 Introduction
lesson2 Discontinuous groups and regular covering maps
lesson3 Local geometric structures and discontinuous group
lesson4 Proper actions
lesson5 Homogeneous spaces
lesson6 Proper actions on homogeneous spaces
lesson7 Cartan projections of linear reductive groups
lesson8 Kobayashi's properness criterion
lesson9 Coarse spaces
lesson10 Coarsely equivalent maps
lesson11 Asymptotically disjoint pairs
lesson12 Coarsely equivalent maps and Asymptotically disjoint pairs
lesson13 Cartan projections and Coarsely equivalent maps
lesson14 Kobayashi's properness criterion in Coarse geometry
lesson15 Summary

Homework will be assigned in the lecture.  
No textbook.
Reference books:
T. Kobayashi, Discontinuous groups for non-Riemannian homogeneous spaces, Mathematics Unlimited---2001 and Beyond (B. Engquist and W. Schmid, eds.), Springer-Verlag, 2001.
J. Roe, Lectures on Coarse geometry (University Lecture Series), AMS, 2003. 
PC or AV used in
(More Details)  
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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