Appears in collection : 2024 - T2 - WS1 - Low Dimensional Actions

My talk will follow a joint work with Maximiliano Escayola, devoted to the study of critical regularities for nilpotent group actions. The questions of critical regularities have been studied by many authors in many different contexts: starting from the classical Denjoy theorem and example, there are works by M. Herman, J.-C. Yoccoz, N. Kopell, T. Tsuboi, D. Pixton, B. Farb, J. Franks, K. Parkhe, B. Deroin, A. Navas, C. Rivas, E. Jorquera, Kim, T. Koberda, any many others. We’ll be describing the critical regularity for nilpotent group actions in algebraic terms, introducing some new technique for establishing the bounds.