WSA33000 Topics in Geometry A

Hiroshima University Syllabus

Japanese

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
（Katakana）タヨウキカトクロンエー

Subject Name in
English Topics in Geometry A

Instructor FUJIMORI SHOICHI,OKUDA TAKAYUKI

Instructor
(Katakana) 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
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 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.

Text/Reference
Books,etc. 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
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.

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 （Katakana）	タヨウキカトクロンエー
Subject Name in English	Topics in Geometry A
Instructor	FUJIMORI SHOICHI,OKUDA TAKAYUKI
Instructor (Katakana)	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 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 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.
Text/Reference Books,etc.	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 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.

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