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 uses differential equations to model how people move between law-abiding life, crime, and incarceration. By simulating rehabilitation, overcrowding, and policy changes, the work shows how prisons can sometimes produce crime—and how evidence-based mathematical models can guide smarter decisions that reduce crime and build safer communities.

This talk explains research that teaches legged robots how to walk reliably using machine learning, computer vision, advanced control theory, and Lyapunov-based safety guarantees. By improving robot stability on complex terrain, the work moves us closer to versatile, household multi-purpose robots capable of performing everyday chores safely and independently.

This research develops mathematical models to understand how honeybee clusters survive extreme cold without their hive. Using temperature and density equations, the model predicts how bees move, generate heat, and form insulating layers. Accurate simulations could reduce harmful field experiments and provide biologists with a powerful tool for studying bee behaviour.

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.