2025 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry D1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Nobuhiro Honda
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MTH.B408
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 4Q
- Syllabus updated
- Mar 19, 2025
- Language
- English
Syllabus
Course overview and goals
To learn several commonly used topics in geometry
Course description and aims
Understand the proof of Sard theorem, Newlander-Nirengerg integrability theorem, and Ehresmann's fibration theorem
Understand the notions of vector bundles, connections, and the characteristic classes
Keywords
Sard's theorem, Ehresmann's fibration theorem, integrability theorem of almost complex structure, vector bundle, curvature, Chern-Weil theory
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Sard theorem 1 | Details will be provided during in class. |
| Class 2 | Sard theorem 2 | Details will be provided in class. |
| Class 3 | Ehresmann's fibration theorem | Details will be provided in class. |
| Class 4 | Newlander-Nirenberg integrability theorem | Details will be provided in class. |
| Class 5 | vector bundle and connection | Details will be provided in class. |
| Class 6 | curvature | Details will be provided in class. |
| Class 7 | Chern-Weil theory | Details will be provided in class. |
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.
Reference books, course materials, etc.
S. Sternberg "Lectures on differential geometry" Prentice-Hall
J. Milnor, "Topology from differentiablel viewpoint" Princeton Landmarks in Mathematics
C. Taubes "Differential Geometry" Oxford Mathematics
Evaluation methods and criteria
Assignments (100%).
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
Prerequisites
It is assumed that the student understands the content of the three courses listed above