Mathematics

In this course we will give an introduction to gauge theory on smooth 4-manifolds and to its applications in differential topology and algebraic geometry. The following themes are supposed to be covered: 

1.  Principal Bundles and Connections
2.  Curvature and Characteristic Classes
3.  The Space of Connections
4.  The ASD Equations and the Moduli Space
5.  Compactness and Gluing Theorems
6. Definite intersection forms
7. The Donaldson polynomial invariants
8. The Connected Sum Theorem
9. The Kobayashi-Hitchin correspondence
10. Differentiable structures on complex algebraic surfaces