# Seminário Geometria em Lisboa

### $C^0$-rigidity in symplectic topology

The Gromov-Eliashberg Theorem states that the $C^0$-limit of a sequence of symplectomorphisms is symplectic. This rigidity phenomenon motivated the study of $C^0$ symplectic geometry which is concerned with continuous analogs of classical objects. In a joint work with V. Humilière and S. Seyfaddini, we showed that coisotropic submanifolds together with their characteristic foliations are also $C^0$ rigid. I will discuss this result and in particular I will explain how it relies on continuous analogs of dynamical properties satisfied by coisotropics. Then I will discuss consequences of this rigidity phenomenon.