On April 11, 2026, Professor Alberto Bressan, Eberly Family Chair in Mathematics at Pennsylvania State University, presented a lecture titled "Modeling Traffic Flow." at Zhiyuan College.

Professor Bressan systematically introduced mathematical approaches to describing vehicle movement, ranging from microscopic particle models using ordinary differential equations to macroscopic continuum models based on partial differential equations and conservation laws.

In the second half of the talk, Bressan discussed advanced models and emerging questions in traffic research. He presented a two-flux conservation law incorporating "acceleration" and "deceleration" modes to better capture the formation of stop-and-go waves on highways. From a decision-theoretic perspective, he also interpreted traffic flow as a collective game among drivers choosing departure times and routes, linking the problem to the existence and stability of Nash equilibria.

During the interactive session, faculty and students engaged in a lively discussion on model assumptions, connections between micro- and macro-scale models, and open problems in traffic flow research. Professor Bressan encouraged the audience to begin with clear, concise mathematical questions and gradually deepen their understanding of complex real-world systems.

The ZY-INS Salon series will continue to invite distinguished scholars from around the world to share cutting-edge research and inspire students to explore complex systems through mathematical thinking.