Title: Warped cones violating the coarse Baum--Connes conjecture

Abstract: I will report on work establishing a conjecture of Drutu and Nowak that the coarse assembly map is not surjective for warped cones over actions with a spectral gap. On the one hand, this yields some counterexamples to the coarse Baum--Connes conjecture not coarsely equivalent to a family of graphs. On the other, by a work of Vigolo in cases of most interest these spaces are QI to expanders, some of which I showed to be expanders with respect to Banach spaces of non-trivial type.