The tangent method: a painless path to computing the arctic curve of tiling problems

par Emmanuel Guitter (IPhT, CEA Saclay)

vendredi 14 févr. 2020, 10:15 → 12:45 Europe/Paris

salle 435 (ENS de Lyon, site Monod)

Tiling problems are known to exhibit the so-called arctic curve phenomenon, with the emergence of a sharp frontier beyond which the configurations are fully frozen. The tangent method, invented by Colomo and Sportiello, is a geometrically elegant and conceptually simple approach which allows to compute without pain the shape of the arctic curve in numerous tiling problems. I will present the method in one of its simplest realization, that to the domino tiling of the Aztec diamond and show how to easily recover the arctic circle in this case. I will then discuss results for natural extensions of this problem. This presentation is based on some joint work with P. Di Francesco.

After the break, the second talk will be on :

More arctic curves from the tangent method: the case of the 20-vertex model

I will discuss in details how to obtain explicitly the arctic curves of a number of specific non-intersecting or osculating path models via the tangent method. The models include non-intersecting paths with an arbitrary distribution of starting points as well as osculating path configurations describing the celebrated 20-vertex model (the ice model on the triangular lattice) with particular domain wall boundary conditions. This is a joint work with P. Di Francesco and B. Debin.