We are interested in the spectral representation of hyperuniform point processes in $\mathbb{R}^d$. A stationary point process is hyperuniform when the variance of the number of points in a large observation window grows more slowly than the window volume. Equivalently, the structure factor $S(k)$ — obtained from the Fourier transform of the total covariance measure — satisfies $S(k) \to 0$ as $|k| \to 0$.
We are looking for collaborators to study spectral characterisations, optimal-transport couplings, and Laplace-type operators associated with such point processes.