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- Academic unit or major
- Mathematics
- Instructor(s)
- Tanabe Masaharu
- Class Format
- Lecture (ZOOM)
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H137)
- Group
- -
- Course number
- ZUA.C331
- Credits
- 1
- Academic year
- 2020
- Offered quarter
- 1Q
- Syllabus updated
- 2020/9/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
A Riemann surface is a two-real-dimensional manifold with holomorphic coordinate transformations.
The theory of Riemann surfaces has been a source of inspiration and examples for many fields of mathematics.
We will study the most important theorems concerning closed Riemann surfaces: the Riemann-Roch theorem,
Abel’s theorem, and the Jacobi inversion theorem.
This course will be completed with ''Advanced topics in Analysis B'' in the next quarter.
In this course, our goal is to understand and hence to prove the Riemann-Roch theorem.
Student learning outcomes
At the end of this course, students are expected to understand the Riemann-Roch theorem.
Keywords
Riemann surfaces, the Riemann-Roch theorem
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Riemann surfaces | Details will be provided during each class session. |
| Class 2 | Topology of Riemann surfaces | |
| Class 3 | Differential forms | |
| Class 4 | Harmonic differetials, holomorphic differetials | |
| Class 5 | Bilinear relations | |
| Class 6 | Divisors | |
| Class 7 | The Riemann-Roch theorem |
Out-of-Class Study Time (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 in particular
Reference books, course materials, etc.
H. M. Farkas and I. Kra, Riemann surfaces, GTM 71, Springer-Verlag
Assessment criteria and methods
Assignments. Details will be announced during the session.
Related courses
- ZUA.C301 ： Complex Analysis I
- MTH.C301 ： Complex Analysis I
- MTH.C302 ： Complex Analysis II
- MTH.C402 ： Advanced topics in Analysis B
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None
Other
None in particular
