From stable trapping to turbulence: Nonlinear dynamics in gravitational systems. Turbulence is a universal feature in many nonlinear systems, with broad applications across physics, from classical fluid mechanics to gravitational dynamics. Understanding the dynamics of spacetimes with stable trapping — regions where energy can be confined for long times — is crucial for exploring complex gravitational systems. In this talk, Cardenas-Avendano will describe the behavior of nonlinear scalar waves on a simple model spacetime that admits such trapping. While linear waves exhibit slow decay, we show that nonlinear waves lead to turbulent behavior due to energy cascading to higher modes. Our results offer insights into the stability of exotic spacetimes in general relativity, potentially ruling out certain types of instability. More details.