In the second lecture, I will start by giving a more algebraic interpretation of the key ingredients needed in the construction of the conformal Cartan connection. In this interpretation, one then obtains a proof for existence and uniqueness of a Cartan description for all parabolic geometries and several other filtered G-structures.
I will then discuss several general constructions relating Cartan geometries of different type (Fefferman constructions, extension functors, and holonomy reductions of Cartan geometries). Finally, I will discuss some general tool for the construction of differential operators naturally associated to Cartan geometries.