Kaleidoscopic groups are infinite permutation groups recently introduced by Duchesne, Monod, and Wesolek by analogy with a classical construction of Burger and Mozes of subgroups of automorphism groups of regular trees. In contrast with the Burger-Mozes groups, kaleidoscopic groups are never locally compact and they are realized as groups of homeomorphisms of Wazewski dendrites (tree-like, compact spaces whose branch points are dense). The input for the construction is a finite or infinite permutation group Gamma and the output is the kaleidoscopic group K(Gamma).

In this talk, I will discuss recent joint work with Gianluca Basso, in which we explain how these groups can be viewed as automorphism groups of homogeneous structures and characterize the universal minimal flow of K(Gamma) in terms of the original group Gamma.