## Mendes Oulamara [1]

The six-vertex model, first introduced to model ice, has deep connections with many planar statistical physics models (the Ising model, dimers, percolation, loop O(n) models...). Its height function representation is a random function h:ZxZ -> Z such that the height of two neighbouring points differ by 1 or -1. It can hence be seen as a random discrete surface. Now, assume that one sets this function to be zero on the boundary of some planar domain D, how does the height fluctuate inside the domain? Is it typically flat or rough (i.e. it has unbounded variance)? In this joint work with Hugo Duminil-Copin, Alex Karrila and Ioan Manolescu, we show that estimates on the free energy of the model can be translated into probabilistic statements on the geometry of the height function. (arxiv.org/abs/2012.13750)