Non-Euclidean geometry in nature

TL;DR

This paper explores how non-Euclidean geometry manifests in natural systems, analyzing plant shapes and sparse random graphs to understand their geometric and spectral properties.

Contribution

It introduces a unified perspective on non-Euclidean geometry's role in physical systems, linking plant morphology and graph spectral statistics.

Findings

Optimal embedding of plant leaves in 3D space

Spectral statistics of sparse random matrix ensembles

Manifestation of non-Euclidean geometry in physical systems

Abstract

I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random graphs. For these systems I discuss the following interlinked questions: (i) the optimal embedding of plants leaves in the three-dimensional space, (ii) the spectral statistics of sparse random matrix ensembles.