Abstract: In my talk I will discuss the classification of finite simple
groups that act transitively and with fixity 4 on some set, which means
that every non-trivial element fixes at most 4 points and there exists a
non-trivial element with exactly 4 fixed points. An emphasis of the talk
lies upon the case when point stabilizers have odd order divisible by 3.
This is part of a project initiated by Kay Magaard and worked on
together with Barbara Baumeister, Patrick Salfeld and Rebecca Waldecker.