8K200201 Introduction to homotopy theory & its applications to physical systems

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School International Institute for Sustainability with Knotted Chiral Meta Matter (Courses for Graduate Students)

Lecture Code 8K200201 Subject Classification Specialized Education

Subject Name Introduction to homotopy theory & its applications to physical systems

Subject Name
（Katakana）イントロダクション　トゥ　ホモトピー　セオリー　アンド　イッツ　アプリケーションズ　トゥ　フィジカル　システムズ

Subject Name in
English Introduction to homotopy theory & its applications to physical systems

Instructor INOUE KATSUYA

Instructor
(Katakana) イノウエ　カツヤ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  First Semester

Days, Periods, and Classrooms (1st) Inte

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Venue: Seminar Room  (SCIENCE KNOT 2F）

Credits 2.0 Class Hours/Week 　 Language of Instruction E : English

Course Level 5 : Graduate Basic

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 07 : Chemistry

Eligible Students For students registered International Program for Collaborative Sciences Enabling the Future（WPI-SKCM2 Fellows）

Keywords Homotopy theory, condensed matter physics, material science, liquid crystals, ordered media

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 This course on applications of homotopy theory intends to introduce fundamentals of topological classification and analysis of field configurations as applied to ordered media like liquid crystals. It will provide a background to mathematical methods and the overview applications of these methods   in both soft and hard condensed matter physics, material science, as well as other types of physical systems. The course is intended for graduate students.

Class Schedule We invite Prof. Hirokazu Hori (Emeritus Professor at the University of Yamanashi) as a lecturer, and he will give lectures.

Lesson 1 Physical systems, ordered media and order parameter spaces (Inoue)
Lesson 2 Anticipated physical phenomena based on homotopy theory predictions (Hori&Inoue)
Lesson 3 Importance of topological thinking and imaging in natural science (Hori)
Lesson 4 Introduction to category theory and homological algebra (Hori)       　
Lesson 5 Applications of homological algebra for description of functionalities (Hori)
Lesson 6 Description of dynamical system in environment (Hori)
Lesson 7 Manifold and fiber structures (Hori)
Lesson 8 Simplical sets, fibrations, geometric realization (Hori)
Lesson 9 Topological properties of braid and knots (Hori)
Lesson 10 Space-time picture and general description of functionalities (Hori)
Lesson 11 Functionalities of a system in environment (Hori)
Lesson 12 Phenomenology on non-equilibrium open systems (Hori)
Lesson 13 Topological properties in natural science (Hori)
lesson 14 Introduction to flag manifold and Schubert calculus (Hori)
lesson 15 General mathematical viewpoints and descriptions of functionalities (Hori&Inoue)

【Class Schedule】
① Lesson 1～Lesson 4
　  June 12 (Fri) 8:45 (1st Period)～16:05 (4th Period)
② Lesson 5～Lesson 7
    June 19 (Fri) 10:30 (2nd Period)～16:05 (4th Period)
③ Lesson 8～Lesson 9
    June 26 (Fri) 10:30 (2nd Period)～14:20 (3rd Period)
④ Lesson 10～Lesson 11
    July  3 (Fri) 10:30 (2nd Period)～14:20 (3rd Period)
① Lesson 12～Lesson 15
　  July 10 (Fri) 10:30 (2nd Period)～17:50 (5th Period)

【Venue】Seminar Room  (SCIENCE KNOT 2F）

Text/Reference
Books,etc. Indicated in the first class

PC or AV used in
Class,etc.

(More Details)

Learning techniques to be incorporated

Suggestions on
Preparation and
Review Take note

Requirements

Grading Method Report

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	2026Year	School/Graduate School	International Institute for Sustainability with Knotted Chiral Meta Matter (Courses for Graduate Students)
Lecture Code	8K200201	Subject Classification	Specialized Education
Subject Name	Introduction to homotopy theory & its applications to physical systems
Subject Name （Katakana）	イントロダクション　トゥ　ホモトピー　セオリー　アンド　イッツ　アプリケーションズ　トゥ　フィジカル　システムズ
Subject Name in English	Introduction to homotopy theory & its applications to physical systems
Instructor	INOUE KATSUYA
Instructor (Katakana)	イノウエ　カツヤ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, First Semester
Days, Periods, and Classrooms	(1st) Inte
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
Venue: Seminar Room (SCIENCE KNOT 2F）
Credits	2.0	Class Hours/Week		Language of Instruction	E : English
Course Level	5 : Graduate Basic
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	07 : Chemistry
Eligible Students	For students registered International Program for Collaborative Sciences Enabling the Future（WPI-SKCM2 Fellows）
Keywords	Homotopy theory, condensed matter physics, material science, liquid crystals, ordered media
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	This course on applications of homotopy theory intends to introduce fundamentals of topological classification and analysis of field configurations as applied to ordered media like liquid crystals. It will provide a background to mathematical methods and the overview applications of these methods in both soft and hard condensed matter physics, material science, as well as other types of physical systems. The course is intended for graduate students.
Class Schedule	We invite Prof. Hirokazu Hori (Emeritus Professor at the University of Yamanashi) as a lecturer, and he will give lectures. Lesson 1 Physical systems, ordered media and order parameter spaces (Inoue) Lesson 2 Anticipated physical phenomena based on homotopy theory predictions (Hori&Inoue) Lesson 3 Importance of topological thinking and imaging in natural science (Hori) Lesson 4 Introduction to category theory and homological algebra (Hori) 　 Lesson 5 Applications of homological algebra for description of functionalities (Hori) Lesson 6 Description of dynamical system in environment (Hori) Lesson 7 Manifold and fiber structures (Hori) Lesson 8 Simplical sets, fibrations, geometric realization (Hori) Lesson 9 Topological properties of braid and knots (Hori) Lesson 10 Space-time picture and general description of functionalities (Hori) Lesson 11 Functionalities of a system in environment (Hori) Lesson 12 Phenomenology on non-equilibrium open systems (Hori) Lesson 13 Topological properties in natural science (Hori) lesson 14 Introduction to flag manifold and Schubert calculus (Hori) lesson 15 General mathematical viewpoints and descriptions of functionalities (Hori&Inoue) 【Class Schedule】 ① Lesson 1～Lesson 4 　 June 12 (Fri) 8:45 (1st Period)～16:05 (4th Period) ② Lesson 5～Lesson 7 June 19 (Fri) 10:30 (2nd Period)～16:05 (4th Period) ③ Lesson 8～Lesson 9 June 26 (Fri) 10:30 (2nd Period)～14:20 (3rd Period) ④ Lesson 10～Lesson 11 July 3 (Fri) 10:30 (2nd Period)～14:20 (3rd Period) ① Lesson 12～Lesson 15 　 July 10 (Fri) 10:30 (2nd Period)～17:50 (5th Period) 【Venue】Seminar Room (SCIENCE KNOT 2F）
Text/Reference Books,etc.	Indicated in the first class
PC or AV used in Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	Take note
Requirements
Grading Method	Report
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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