The unpredictable higher dimensional Thompson groups

Higher dimensional Thompson groups, first introduced by Brin, are groups of homeomorphisms of powers of the Cantor set. Their description is similar to those of the classical Thompson groups F,T,V but elements present substantial differences, such as having chaotic dynamics. In this talk we will define these groups and begin discussing some known properties, such as finiteness properties and undecidability ones. We then report on recent work on computing centralizers of elements using diagrams and dynamics and what makes them elusive for many elements (this is joint work with James Belk, Conchita Martinez-Perez and Brita Nucinkis).