This talk contains two parts. The second part present a generalization of the Gromov-Wasserstein distances to the space of unbalanced metric measures spaces. The first part presents an estimator for optimal tranport distances and potentials between two smooth distributions. This almost statistically optimal estimator is defined through a sum-of-squares method in reproducing kernel Hilbert spaces which gives a finite dimensional SDP problem. This result is however asympotically satisfied, or more precisely the constant are exponential in the dimension.