Alberto Bressan Distinguished Lecturer
Modeling Traffic Flow
Alberto Bressan
Department of Mathematics
The Pennsylvania State University
Thursday, March 5, 2026
4:00 pm
300 Strong Hall
Reception at 3:30 pm, 406 Snow Hall
A mathematical description of traffic flow can be achieved by particle models, in terms of a large number of ODEs describing the position of each car, or by continuum models, in terms of a PDE for the traffic density. After a general introduction, the talk will cover some recent models of traffic flow, and the new mathematical problems that they generate.
The first part of the talk will focus on a new macroscopic model described by a conservation law with two fluxes, depending on whether the drivers are in “acceleration mode” or in “deceleration mode”. Such a model can account for the random creation of stop-and-go waves along a highway.
Vehicular traffic can also be analyzed from the point of view of decision theory. Indeed, daily traffic patterns arise as the outcome of the decisions of a large number of drivers, who choose their departure time and route to destination in an “optimal” way. In the second part of the talk, the existence and dynamic stability of Nash equilibria will be discussed, together with some open problems.
Alberto Bressan is the Eberly Family Chair Professor of Mathematics at The Pennsylvania State University. He obtained his Ph.D. in mathematics from the University of Colorado at Boulder under the supervision of Jerrold Beberne in 1982. After postdoctoral research at the University of Padua and the Mathematics Research Center of the University of Wisconsin-Madison, he became an associate professor at the University of Colorado at Boulder in 1986. Bressan received a full professorship at the Scuola Internazionale Superiore di Studi Avanzati, SISSA, in Trieste, Italy in 1991. In 2003, he moved to The Pennsylvania State University to assume a full professorship there, and he was appointed to the Eberly Family Chair in 2008. He is director of the Center for Computational Mathematics and Applications at the Department of Mathematics.
His primary field of research is mathematical analysis including hyperbolic systems of conservation laws,impulsive control of Lagrangian systems, and non-cooperative differential games. He currently serves on the editorial board of seventeen mathematical journals.
He became a member of the Accademia Nzionale dei Lincei, Rome (2022), fellow of the American Mathematical Society, AMS (2012), member of the Royal Norwegian Society of Sciences and Letters, Trondheim (2011), and member of the Accademia di Scienze e Lettere, Istituto Lombardo, Milan (2011). He won the Bôcher Memorial Prize from the AMS in 2008 and the Analysis of Partial Differential Equations Prize of the SIAM in 2007 for his work in PDEs (with Stefano Bianchini).
Additional honors include the A. Feltrinelli prize for Mathematics, Mechanics and Applications of theAccademia Nazionale dei Lincei in Rome (2006); Luigi and Wanda Amerio prize, Accademia di Scienze e Lettere, Istituto Lombardo. Milan, 2010; and Gaetano Fichera prize for mathematical analysis, Unione Matematica Italiana. Bologna, 2011. Bressan was invited to give a plenary talk at the International Congress of Mathematicians at Beijing in August 2002.