Field theory
Global Analysis
Prof. Dr. D. Grieser, Institute of Mathematics
University of Oldenburg
Videos
- 04.04.2013 Introduction, Manifolds, examples
- 05.04.2013 Tangent space, differential of functions and maps, tangent bundle
- 11.04.2013 Vector fields (a) Vector fields (b)
- 12.04.2013 Lie bracket (a) Lie bracket (b)
- 18.04.2013 Lie derivative (a) Differential forms (b)
- 19.04.2013 Tensors
- 25.04.2013 Exterior product/Diffential forms
- 26.04.2013 Exterior derivative/Orientation on manifolds
- 02.05.2013 Integration of differential forms
- 03.05.2013 Stokes' Theorem (a) Scalar product (b)
- 10.05.2013 Hodge star (a) grad,div,rot (b)
- 16.05.2013 Gauss Theorem/Lie derivative of differential forms
- 17.05.2013 De Rham cohomology (a) De Rham cohomology (b)
- 23.05.2013 Homological algebras; homotopies
- 24.05.2013 Homotopy invarivants(a) Poincare Lemma; Brouwers fixed point theorem(b)
- 30.05.2013 Computation of cohomology: Mayer-Vietoris sequence
- 31.05.2013 Computation of cohomology(continued)(a) Homology(b)
- 06.06.2013 Computation of homology
- 07.06.2013 Periods of comohology; Hodge Theorem(a) (continued)(b)
- 13.06.2013 Hodge Theory
- 14.06.2013 Hodge Theorem(continued)(a) Vector bundles(b)
- 20.06.2013 Connections on vector bundles
- 21.06.2013 Curvature(a) (continued)(b)
- 27.06.2013 Parallel Transport(a) (continued)(b)
- 28.06.2013 Cevi-Levita connection(a) (continued)(b)
- 04.07.2013 Symmetries of curvature/Geodesics
- 05.07.2013 Jacobi fields(a) (continued)(b)