In this talk we show that, in fact, for the generic choice of the pair $(f_0,f_1),$ there exists an integer $N>0$ such that the control $u$ associated to any time-extremal trajectory admits at most Fuller times of order $N$. In particular, $u$ is smooth out of a set of measure zero. This is a joint work with M. Sigalotti (CMAP, Ecole Polytechnique).
Bio: Francesco Boarotto was born in Verona, Italie, in 1988. He received the Master's degree in mathematics from the University of Padou, Italie, in 2012 and the Ph.D degree from SISSA, Trieste, Italie, in 2016. Since then he has been post-doc in CMAP - Ecole Polytechnique. His research interests include geometric control theory and sub-Riemannian geometry.