Date/Time
Date(s) - 26/09/2025
1:30 pm - 2:30 pm

Location: HH-410

Title: On the emergence of almost-honeycomb structures in low-energy planar clusters

Abstract: Several commonly observed physical and biological systems are arranged in shapes that closely resemble a tessellation of the plane by regular hexagons (honeycomb cluster). Although these shapes are not always the direct product of energy minimization, they can still be understood, at least phenomenologically, as low-energy configurations. In this talk, explicit quantitative estimates on the geometry of every such low-energy planar cluster are provided, showing in particular that the vast majority of the chambers of such clusters must be generalized polygons with six edges, and closely resemble regular hexagons. Part of our argument is a detailed revision of the estimates behind the global isoperimetric principle for honeycomb clusters due to Hales. This talk is based on joint work with M. Caroccia and F. Maggi.