In this talk I will discuss the "Robin-Neumann" gaps (RN gaps), that is, the differences between the Robin and the Neumann eigenvalues of a surface. After an introduction of this concept I will discuss several recent results on the RN gaps corresponding to different surfaces, and, in particular, the ergodic billiards. Some open questions pertaining to RN gaps will be put forward. This talk is based on joint works with Zeev Rudnick, Nadav Yesha and Alexander Pushnitski.
