| 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
（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, 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
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 |
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 |
Text/Reference
Books,etc. |
Indicated in the first class |
PC or AV used in
Class,etc. |
|
| (More Details) |
PC, presentation slides, research equipment for hands-on experience |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
You are expected to review after each lecture. Often, we will assign exercises. |
| Requirements |
|
| Grading Method |
Homework (30%), projects (30%) and exams (40%) |
| 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. |