2025 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Special lectures on current topics in Mathematics C
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Shouhei Honda / Toshiaki Hattori
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Intensive
- Class
- -
- Course Code
- MTH.E633
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 1Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
The study of singular spaces related to Ricci curvature via Geometric Analysis is quickly developing with deep connections with other subjects including Algebraic Geometry, Complex Geometry and Probability. The course description is to provide its basics, together with recent developments about singular Kaehler spaces if time permits.
We can understand how to drop the smoothness in the previous studies, including Calculus.
Course description and aims
The goal is to understand the importance of the notion of Gromov-Hausdorff convergence with the benefits coming from non-smooth Geometric Analysis.
Keywords
Ricci curvature, Laplacian, Gromov-Hausdorff convergence, Kaehler metric, Einstein manifold, (Geometric) Measure Theory, and Metric Geometry
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | We will explain the following topics. - Gromov-Hausdorff convergence - Introduction to Riemannian Geometry - Calculus on Metric Measure Space - RCD Space and Optimal Transportation Theory - Almost Smooth Space, RCD condition, and Singular Kaehler metric | 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)
None required.
Reference books, course materials, etc.
We will provide possible references in the lectures.
Evaluation methods and criteria
Assignments (100%).
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
Prerequisites
None required.