Tentative Schedule of the course
Week 1: Review on the basic definitions differential forms, vector bundles, principal bundles, associated bundles
Week 2: Connections, covariant derivatives, and curvatures.
Week 3: Foliations and Frobenius theorem.
Week 4-5: Review on basic Lie group theory, decomposition of semi-simple Lie algebras
Week 6: Fundamental theorem of calculus and the structure equations.
Week 7: Basic definitions in Cartan geometry, i.e. Cartan connections, curvatures and gauges.
Week 8: First basic example: Cartan bundles of Riemannian geometry.
Week 9-10: Introduction to parabolic geometries. Regularity and Normality.
Week 11: Development map and distinguished curves.
Week 12-13: Examples in -graded geometries: projective and conformal.
Week 14: Examples in -graded geometries: parabolic contact geometry.