| Date | Topics |
|---|---|
| 28.02 | Introduction and presentation of the topics |
| 06.03 | Connections, curvature, the Yang-Mills functional, gauge invariance, Coulomb gauge |
| 13.03 | Bianchi and Yang-Mills equations, Functional analysis: Sobolev embeddings, Calderón-Zygmund theory, Hodge decomposition |
| 20.03 | Adams-Morrey embeddings, regularity results for quasilinear elliptic systems (Ladyzhenskaya) |
| 27.03 | Regularity results for quasilinear elliptic systems (Ladyzhenskaya), application to the regularity of Yang-Mills fields in Coulomb gauge |
| 10.04 | Coulomb gauge and Uhlenbeck gauge extraction theorem |
| 17.04 | Uhlenbeck gauge extraction theorem, regularity of Yang-Mills fields, concentration compactness |
| 24.04 | Point removability for Yang-Mills fields |
| 08.05 | Lorentz spaces: definition, duality, improved Sobolev embeddings |
| 15.05 | Energy quantization for Yang-Mills fields |
| 22.05 | Sobolev maps between manifolds, density of smooth functions, approximation of cocycles, counterexamples |
| 29.05 | Strong and weak approximation in Sobolev spaces between manifolds |
Functional Analysis 1+2
Differential Geometry 1+2
The second parts (FA II and DG II) can be taken in parallel in the Spring Semester 2024.