Discrete Math Seminar: Jan de Gier
Topic
The critical surface adsorption for self-avoiding walks on the honeycomb lattice is $1+\sqrt{2}$
Speakers
Details
Abstract
In 2010 Duminil-Copin and Smirnov (DCS) proved rigorously that the growth constant for self-avoiding walks on the honeycomb lattice is equal to $\sqrt{2+\sqrt{2}}$, a value conjectured by Nienhuis in 1982. One of the main ingredients in DCS's proof is a finite lattice identity for generating functions obtained from a discretely holomorphic observable. I will discuss an extension of their proof to include boundary weights, and hence a method for establishing the critical fugacity for the adsorption transition for self avoiding walks.
