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.
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.
anti-self-dual equations, instantons, moduli spaces, Uhlenbeck compactness, bubbling analysis
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
This is a standard lecture course. There will be some assignments.
Course schedule | Required learning | |
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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. |
None required.
Details will be provided during each class session.
Assignments (100%).
Basic knowledge about smooth manifolds