Duration: 1:02:26

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We will present the proof of a conjecture of B. Nienhuis on the number of self-avoiding walks on the honeycomb lattice. More precisely, we will prove that the connective constant of the lattice equals the square root of (2+\sqrt{2}). This theorem is the first step towards a deeper understanding of self-avoiding walks. We will state some conjectures on the scaling-limit behavior of these walks.