Aggregates, such as colloids or bacteria, exhibit fascinating behaviors like transient formation and emergent motion. These dynamics are driven by diverse physical forces including interparticle interactions, self- propulsion, and thermal noise. To characterize dynamic properties in these systems, particularly their collective out-of-equilibrium dynamics, we lack appropriate metrics. This limits our understanding of the mechanisms underlying aggregate behaviors. To define new relevant metrics, we explore the potential of a new analysis technique, called ``Countoscope’’, that tracks the number of particles in virtual observation volumes of the system over time. These counts fluctuate, due to diffusion, motility, or attraction. We can analyze these number fluctuations to disentangle the different processes and quantify the underlying collective dynamics. This internship will combine theoretical modeling to define new metrics and interpret measured behavior, especially as we apply this to the microscopy analysis of colloidal systems (in particular in collaboration with Alice Thorneywork, Oxford University). In particular, we seek to explore high-order contributions (e.g second-, third-, or fourth-order correlation functions), to uncover deep dynamic signatures of collective behavior.