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.