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- Academic unit or major
- Mathematics
- Instructor(s)
- Matsuo Shinichiro Gomi Kiyonori
- Class Format
- Lecture (Livestream)
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive ()
- Group
- -
- Course number
- ZUA.E333
- Credits
- 2
- Academic year
- 2022
- Offered quarter
- 2Q
- Syllabus updated
- 2022/3/16
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This is an introductory course on geometric analysis. We will fous on the bubbling analysis of Uhlenbeck and explain her compactness theorem.
Through the detailed explanation of the Uhlenbeck compactness, we will become familiar with many concepts of geometric analysis.
Student learning outcomes
Be familiar with connections, curvature, and gauge transformations.
Be familiar with the anti-self-dual equations and instantons.
Be familiar with Sobolev spaces.
Be familiar with conformal invariance and bubbling analysis.
Keywords
anti-self-dual equations, instantons, moduli spaces, Uhlenbeck compactness, bubbling analysis
Competencies that will be developed
| ✔ 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/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | We will cover the following topics: 1. Connections, curvatures, and gauge transformations. 2. The anti-self-dual equations and instantons 3. Bubbling analyisis 4. Global slices and the Coulomb gauge 5. Curvature is proper. 6. Mean-value theorem, Chern-Simons invariants, and the anti-self-dual equations 7. The proof of the Uhlenbeck compactness theorem | Details will be provided during each class session. |
Textbook(s)
None required.
Reference books, course materials, etc.
Details will be provided during each class session.
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.B341 ： Topology
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
- MTH.C305 ： Real Analysis I
- MTH.C306 ： Real Analysis II
- MTH.C351 ： Functional Analysis
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basic knowledge about smooth manifolds
