Any group G of permutations can be endowed with the so called standard topology, the group topology in which a system of neighbourhoods of the identity consists of the collection of all fix-point stabilizers of finite sets and in case G is the automorphism group of a countable structure M it is a Polish group topology. For certain classes of highly homogeneous M such as the random graph or the dense linear order this yields interesting examples of Polish groups with remarkable dynamical properties. Here we take a look at the question of minimality, i.e. of whether there are no Hausdorff group topologies on G strictly coarser than the standard topology. We present a couple of new minimality results in case M is the Fraïssé limit of a class with free amalgamation, as well as for the isometry group of the Urysohn space with the point-wise convergence topology. (Joint work with Zaniar Ghadernezhad)