The extremality conjectures for projective and Dowling geometries

Projective geometries and Dowling geometries are classes of matroids. A matroid is extremal if it is an extremal matroid in the polytope studied in the source.

Geometry extremality conjectures.

1. Projective geometries are extremal matroids.
2. Dowling geometries are extremal matroids.

These are proposed as further answers to the problem of identifying meaningful classes of extremal matroids. The source gives no proof or resolution for either assertion.