Hyperuniformity and related topics

Hyperuniformity in point processes refers to the property where large subsamples exhibit low variance in the number of points, as well as in other linear statistics. This phenomenon has been actively studied and sought after for several decades in condensed matter physics and statistical physics, encompassing models from determinantal processes, random matrices, random Gaussian functions or Gibbs measures. The realizations of these processes exhibit remarkable properties, like being rigid or expressible as a perturbed lattice, making them a rich area for mathematical investigation. Their applications extend to various fields, including physics, numerical integration or signal processing. This workshop will provide an opportunity to discuss various mathematical questions related to hyperuniformity, focusing on specific models that exhibit this property, theoretical aspects such as matching or rigidity, and practical issues concerning estimation, simulation, and applications in other fields.