A stability theorem says that a nearly extremal object can be obtained
from an extremal one by small changes. This phenomenon occurs in many
branches of mathematics, we may think of Turán’s theorem and its stability
version due to Erdős and Simonovits, or Segre’s theorem on embedding large
arcs in an oval.
In this talk we present such stability results in finite geometry, in particular
for blocking sets and sets of even type.