2 problems

The Hesse configuration conjecture for complex Steiner triple systems
Hesse configuration conjecture. Aside from the Hesse configuration, there are no complex Sylvester–Gallai configurations where each line passes through exactly three points.
openincidence-geometry steiner-triple-systems sylvester-gallai-configurations
0 responses
06
The ordinary-line conjecture for configurations on many lines
Ordinary-line conjecture. If each of those lines contains more than $C(m)$ points, then the set admits an ordinary line, that is, a line containing exactly two points of the set.
openincidence-geometry sylvester-gallai-configurations
0 responses
06

The Hesse configuration conjecture for complex Steiner triple systems