Hiroshima University Syllabus

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Academic Year 2024Year 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
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
Introduction to homotopy theory & its applications to physical systems
イノウエ カツヤ
Campus Higashi-Hiroshima Semester/Term 1st-Year,  Second Semester,  4Term
Days, Periods, and Classrooms (4T) Inte
Lesson Style Lecture Lesson Style
(More Details)
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
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(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 lesson1 Physical systems, ordered media and order parameter spaces
lesson2 Homological algebra
lesson3 Spaces and homotopy groups
lesson4 Homotopical algebra
lesson5 Simplicial sets
lesson6 Fibrations, geometric realization
lesson7 Simplicial groups, simplicial modules
lesson8 Properness, diagrams of spaces
lesson9 Bisimplicial sets, homotopy limits and colimits
lesson10 Bisimplicial abelian groups
lesson11 Cohomology: an introduction
lesson12 Spectra and stable equivalence
lesson13 Basic properties of stable homotopy theory
lesson14 Samples of homotopy theory applications in soft and hard condensed matter physics
lesson15 Anticipated physical phenomena based on homotopy theory predictions 
Indicated in the first class 
PC or AV used in
(More Details) PC, presentation slides, research equipment for hands-on experience 
Learning techniques to be incorporated  
Suggestions on
Preparation and
You are expected to review after each lecture. Often, we will assign exercises. 
Grading Method Homework (30%), projects (30%) and exams (40%) 
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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