|Résumé||To any group G generated by a finite set X one can associate several languages of words over X, such as the language of normal forms, or of geodesics, and then determine whether such a language is regular, context-free etc. One can also analyze the generating function of the language and determine whether it is rational, algebraic or transcendental. In the last decades several beautiful results have established connections between the algebraic and geometric properties of the group and the languages and generating functions mentioned above.
In this talk I will introduce a language which picks one representative word out of each conjugacy class, and show how one can use tools from various areas to determine the transcendence of the conjugacy growth series in free groups. All the necessary group theoretic concepts will be introduced. |