Mathematical Conversations

Introduced by Stallings in '83, core graphs provide a simple and natural combinatorial-geometric approach to the study of free groups. This approach yields simple elementary proofs to classical results and solutions to various algorithmic problems. It also serves as a crucial tool in various more recent results concerning free groups (e.g. in Mineyev's proof of the Hanna-Neumann conjecture). In the talk I plan to give a flavor of their strength.