Over the past two decades, the field of metamaterials has attracted growing interest from both the scientific community and industry. In recent years, a particularly exciting and promising research direction has emerged: hyperfunctional metamaterials. This concept, in its broadest sense, encompasses systems whose physical and geometrical properties are modulated in time, materials that exhibit multiphysical coupling, and structures that deviate from periodic crystalline order - such as quasicrystals and fractal geometries – or whose response cannot be fully described by local interactions only. The approaches to analyse those systems introduce novel degrees of freedom into the design of metamaterials, enabling the exploration of unconventional physical phenomena and advanced functionalities.
Hyperfunctional metamaterials pave the way for next-generation technologies in wave manipulation, sensing, imaging, energy harvesting, and adaptive systems. Time-modulated metamaterials, for example, are particularly suited for creating tunable sensors that can dynamically respond to real-time environmental changes. Non-reciprocal metamaterials offer significant potential for developing isolators, circulators, and asymmetric waveguides in both electromagnetic and mechanical systems. Meanwhile, aperiodic and non-local metamaterials can efficiently absorb and convert ambient energy - such as electromagnetic waves, mechanical vibrations, or thermal gradients - optimizing energy harvesting across a broad range of frequencies and environmental conditions. The aim of this colloquium is to bring together leading experts from various fields to foster collaboration and accelerate progress in this emerging area. The discussions will focus on key challenges, such as controlling non-reciprocal wave propagation, tuning dynamic responses through multiphysics frameworks, and exploring the emergence of topological effects in non-periodic media. Special attention will be given to mechanical metamaterials, which offer the potential to work at scales accessible to a variety of experimental facilities.

Three central themes will guide the scientific program:

1. Time-modulated metamaterials and metastructures:
   • Non-reciprocity phenomena in time-modulated metamaterials;
   • Parity-time violation;
   • Non-Hermitian and/or nonlinear time-modulated structures;
   • Wave scattering in space-time modulated systems;
2. Multiphysics metamaterials:
   • Willis metamaterials;
   • Thermoelastic metamaterials;
   • Control of fluid flows through metastructures.
3. Aperiodic and non-local metamaterials:
   • Aperiodic quasicrystalline, non-quasicrystalline and non-local metamaterials;
   • Dynamical properties of fractal architected metamaterials;
   • Topological phenomena in non-periodic and non-local structure.