2023 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry B1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Hidetoshi Masai
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Fri (M-102(H115))
- Class
- -
- Course Code
- MTH.B406
- Number of credits
- 100
- Course offered
- 2023
- Offered quarter
- 2Q
- Syllabus updated
- Jul 8, 2025
- Language
- English
Syllabus
Course overview and goals
Understand 3-dimensional hyperbolic geometry by computational methods. In this lecture, we discuss 3-dimensional hyperbolic geometry so that the techniques from verified computation we learned in Advanced topics in Geometry A1 are applicable.
Course description and aims
Understand 3-dimensional hyperbolic geometry via computer.
Keywords
Hyperbolic geometry, non-linear systems of equations
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
A standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Basics of hyperbolic geometry. | Details will be provided during each class session |
| Class 2 | Isometry groups of 2- and 3-dimensional hyperbolic geometry. | Details will be provided during each class session |
| Class 3 | Ideal hyperbolic tetrahedra（e.g. moduli） | Details will be provided during each class session |
| Class 4 | Ideal hyperbolic tetrahedra（e.g. volume formula） | Details will be provided during each class session |
| Class 5 | Gluing equations | Details will be provided during each class session |
| Class 6 | Dehn surgeries and hyperbolic geometry | Details will be provided during each class session |
| Class 7 | Related topics | Details will be provided during each class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
No textbook is set.
Lecture note will be provided.
Reference books, course materials, etc.
・Lectures on Hyperbolic Geometry, Riccardo Benedetti , Carlo Petronio
・Verified Computations for Hyperbolic 3-Manifolds, Neil Hoffman,Kazuhiro Ichihara,Masahide Kashiwagi,Hidetoshi Masai,Shin’ichi Oishi &Akitoshi Takayasu
Evaluation methods and criteria
Assignments (100%).
Related courses
- MTH.B331 ： Geometry III
Prerequisites
Undergraduate-level knowledge of Calculus, Linear Algebra, Group theory, Topology, and Geometry.
Other
There will be no lecture on 14th July.