Probability and Mathematical Physics Seminar

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The hard-core model on bipartite graphs beyond lattices

Speaker: Tyler Helmuth, Durham University

Location: Warren Weaver Hall 1302

Date: Friday, February 20, 2026, 11:10 a.m.

Synopsis:

On Z^2, the hard-core model is a simplification of the physics of the adsorption of atoms onto a crystal surface. At low density the adsorbed atoms are disordered, while they reproduce the crystal structure at high densities.  Mathematically, this corresponds to the study of random independent sets (subsets of vertices, no two of which are neighbours) on Z^2. I'll explain some motivations for studying whether or not a crystallization transition takes place on more general bipartite graphs, and discuss some results in this direction. The main tool for positive results is an adaptation of Pirogov--Sinai theory that applies in wide generality.