# On the proof by Duminil-Copin and Smirnov for the honeycomb lattice growth constant

#### by Tony Guttmann

Institution: MASCOS/Department of Mathematics and Statistics, The University of Melbourne
Date: Mon 8th November 2010
Time: 1:00 PM
Location: Room 213 Richard Berry Building, The University of Melbourne

Abstract: In a recent remarkable paper, H Duminil-Copin and S Smirnov have proved that the growth constant for SAW on the honeycomb lattice is $\sqrt{2+\sqrt{2}},$ confirming a conjecture made nearly 30 years ago by B Nienhuis. The details of the paper are complex, but M. Bousquet-Melou has worked through the paper and prepared a seminar on the topic, which she has sent me. I have worked through her seminar, and also watched on-line a seminar on the topic by Duminil-Copin at Berkely, clarified certain points in private discussion with MBM, and now believe I understand the calculation well enough to present her seminar to you!

For More Information: contact Iwan Jensen. email iwan@ms.unimelb.edu.au