TITLE: Topics in Combinatorial Group Theory (for a short talk).
QUESTION [5 upvotes]: I have started course on combinatorial group theory and supposed to give a short talk/presentation. It would be really helpful if someone can suggest some good/interesting topics to cover.
Thanks

REPLY [2 votes]: I would add to the list some of the problems from identities among relations. (A good article to consult is 
J.-L. Loday, 2000, Homotopical Syzygies, in Une dégustation topologique: Homotopy theory in the Swiss Alps, volume 265 of Contemporary Mathematics, 99 – 127, AMS.
The visual element is good so it makes for a nice presentation. The idea is very simple but then its development requires a bit of care, so again a nice topic to handle. The subtopic of Pictures is also neat.