Disordered hyperuniformity has emerged as a unifying concept at the intersection of mathematics, physics, biology, and materials science. These systems are structurally disordered, like liquids, yet exhibit suppressed long-range density fluctuations [1,2]—anomalies usually associated with crystals or quasicrystals [3]. This unusual combination gives rise to unique physical behaviors, fueling breakthroughs in non-equilibrium physics [4-6], photonic design [7,8], (bio-inspired) materials science [9,10], and many more.

Over the past two decades, hyperuniformity has been discovered across strikingly diverse systems—from colloidal assemblies [11-13] to biological systems [14,15]. This surge in interdisciplinary interest has been mirrored by technological applications, with patents leveraging hyperuniformity for energy-efficient photonics   and biomedical engineering. Yet despite this progress, to the best of our knowledge, only one workshop has focused specifically on hyperuniformity—a striking gap likely due to field’s diversity and breadth. 

In this workshop, we aim to focus on a class of materials—disordered hyperuniform solids—that exhibit emergent properties intermediate between glasses and perfect crystals. First identified in exotic systems like maximally random jammed packings   [16] and certain amorphous systems such as silica [17], these materials are now revealing extraordinary functionalities—from isotropic photonic bandgaps [18] to unusual transport and optical properties [19,20], crystal-like mechanical properties [21,22], and beyond. Yet their theoretical classification and material-specific properties remain unresolved: Do they constitute a distinct thermodynamic phase? How do their mechanical, vibrational, and electronic properties differ from conventional glasses? What (universal) design principles govern their formation (e.g., via quenching, jamming, or bio-inspired assembly)?

Our core emphasis will be on their theoretical and computational understanding, with cross-comparisons to related systems such as fluids, biological tissues, and non-equilibrium assemblies. These comparative case studies will provide a broader context for identifying unifying principles.