Speaker: Francesco Matucci.

Abstract: In their joint paper Bogopolski, Martino and Ventura developed a criterion to study the conjugacy problem of extension of groups. This criterion essentially amounts to studying two extensions of the ordinary conjugacy problem of the base group. We describe the relation between two known characterization of conjugacy in Thompson's group F: the first one, discovered by M.Brin and C.Squier, defines an invariant through the iteration of a given map and the second one, developed by M.Kassabov and the author, involves the construction of actual conjugators through a similar process. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows us study the above decidability problems for F. This is joint work with Jose' Burillo and Enric Ventura.