250516 Florian Zeiser

A common question for geometric structures is that of rigidity, i.e. given two geometric structures sufficiently close, are they equivalent? In this talk we discuss this question for regular foliations on a closed manifold.

In the first part we give an overview of the current state of the art and highlight its relation with the rigidity for group actions. We will see that several rigidity results for foliations require the leaves to be compact.

In an attempt to understand whether such results can be extended to Riemannian foliations, we seek examples of such foliations which are infinitesimally rigid with non-compact leaves. In the second part, we use the relation to group actions to construct infinitesimally rigid Lie foliation with non-compact, dense leaves. This is based on joint work in progress with Stephane Geudens.