Conjugacy, dynamics and subgroups of Thompson's group V

Thompson groups F, T and V were defined by Richard Thompson in connection to his work in logic in the process of building a group with unsolvable word problem and T and V provide the first known examples of finitely presented infinite simple groups. In this talk I will introduce these groups and focus on some properties of V. We give an overview on how to use diagrams to study the conjugacy problem and investigate centralizers. It is of interest to understand the subgroup structure of V since Lehnert and Schweitzer showed that V and all of its subgroups are co-context-free. Co-context-free groups are a natural generalization of groups whose language of the word problem is regular or context-free. We describe known embedding results and explain current directions. (Parts of this talk are joint work with others which will be appropriately cited)