Prof. D. Kotschick:
Seminar on Manifolds: Hodge-de Rham Theory
Sheaves, Cohomology, and the de Rham Theorem
| 31 Oct / 7 Nov | S. Eberle: | Sheaves and Presheaves: 5.1 - 5.15
Definitions, tensor products, fine sheaves |
| 7 / 14 Nov | J. Wehrheim: | Sheaf cohomology: 5.16 - 5.25
Cochain complexes, axioms for sheaf cohomology |
| 21 Nov | J. Kedra: | Classical Cohomology theories: 5.26 - 5.33
Alexander-Spanier Cohom., de Rham Cohom., Singular Cohom., Cech Cohom. |
| 28 Nov | M. Hamilton: | The de Rham theorem: 5.34 - 5.46
Proof |
The Hodge Theorem
| 5 Dec | M. Hamilton: | The Laplace-Beltrami operator: 6.1 -6.14
Definitions, formulation of the regularity theorem, the Hodge Theorem, the Poincaré Theorem |
| 12 Dec | E. Volkov | Analytic preparations: 6.15 - 6.27
Fourier transform, Sobolev spaces, inequalities |
| 19 Dec | V. Strazdin | Proof of the regularity theorems: 6.28
- 6.36
elliptic operators, reduction to the periodic case |
Harmonic Forms on Kähler Manifolds
The following talks are all based on the book Differential Analysis on Complex Manifolds by R. Wells.| 9 / 17 Jan | S. Eberle: | Hermitian Differential Geometry: III.1 and V.1 |
| 17 Jan | S. Eberle: | Harmonic Theory on Compact Manifolds: V.2 |
| 24 Jan | no seminar | |
| 31 Jan | J. Kedra: | Differential Operators on a Kähler Manifold: V.3 |
| 6 Feb | J. Kedra: | The Hodge Decomposition Theorem for Kähler Manifolds: V.4 |
[
Mathematischen
Instituts|
Arbeitsgruppe Differentialgeometrie
und Topologie]