This research develops rigorous mathematical foundations for consensus-based optimization algorithms, where large groups of interacting particles collaboratively search for optimal solutions. Using mean-field theory and propagation of chaos, the work proves long-term stability and improves optimization methods for applications including robotics, aircraft design, and drug discovery under real-world constraints.

This research quantifies the uncertainty in chaotic systems, showing why long-term predictions — from planetary motion to weather patterns — become unreliable. By developing mathematical models that capture chaotic behaviour, the work supports applications in traffic flow, wireless communication, climate forecasting, and disease spread, revealing why some systems are inherently more predictable than others.