Discrete, algebraic and geometric structures appear in many stages of the study in mathematical and computing science. The objective of this course is to describe some advanced topics, and for students to know mathematical structures behind them, based on mathematical backgrounds equivalent to ones provided by college courses of the Department of Mathematical and Computing Science. The theme in 2016 is the geometric group theory.
The students are expected to learn advanced mathematical methods to analyze discrete, algebraic and geometric structures appeared in mathematical and computing science, and to be able to apply them to some practical problems.
discrete structure, algebraic structure, geometric structure, geometric group theory
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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✔ | - | ✔ | ✔ | ✔ |
The course starts with the very beginning of the geometric group theory and covers some of recent advanced topics eventually.
Course schedule | Required learning | |
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Class 1 | Review on Group Theory | Understand the contents covered by the lecture. |
Class 2 | Fundamental Group and Covering Space | Understand the contents covered by the lecture. |
Class 3 | Presentation of Group and Cayley Graph | Understand the contents covered by the lecture. |
Class 4 | Quai-isometry | Understand the contents covered by the lecture. |
Class 5 | Short Course of Constant Curvature Geometry | Understand the contents covered by the lecture. |
Class 6 | Coxeter Group and Linear Representation | Understand the contents covered by the lecture. |
Class 7 | Rright-angled Artin Group and Salvetti Complex | Understand the contents covered by the lecture. |
Class 8 | Subgroup Separability | Understand the contents covered by the lecture. |
Class 9 | Graph of Groups | Understand the contents covered by the lecture. |
Class 10 | Non-positively Curved Cube Complex | Understand the contents covered by the lecture. |
Class 11 | Special Group | Understand the contents covered by the lecture. |
Class 12 | Delta-hyperbolic Space | Understand the contents covered by the lecture. |
Class 13 | Canonical Completion by Wise | Understand the contents covered by the lecture. |
Class 14 | Hyperbolic Group | Understand the contents covered by the lecture. |
Class 15 | Rips Complex and Boundary | Understand the contents covered by the lecture. |
Not specified in particular.
References and some handouts will be provided in the lectures.
Students to write a report on some aspects of the course.
The fundamentals of group theory, point set topology and group action are assumed.