For a finitely generated subgroup H of the free group F_r, the Stallings graph of H is a finite combinatorial graph, whose edges are labeled by r letters (and their inverses), so that paths in the graphs correspond precisely to the words in H. Furthermore, there is a map between the graphs of two subgroups H and J, precisely when one is a subgroups of the other. Stallings theory studies the algebraic information which is encoded in the combinatorics of these graphs and maps. We focus on the question whether H is contained in a free factor of J (which is called a "non-algebraic extension"), and give new algorithms and examples which answer some open questions in the field. No prior knowledge is required.

## Date:

Thu, 20/06/2019 - 10:00 to 11:00