Speaker：
Alberto Bressan, The Pennsylvania State University
Time：
2026.04.01 16:00-17:30
Venue：
Zhiyuan College(Kuang Piu Building), 206
Abstract：
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 stopand-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 stability of Nash equilibria will be discussed, together with some open problems.
Bio：
Alberto Bressan completed his undergraduate studies at the University of Padova, Italy, in 1978, and received a Ph.D. from the University of Colorado, Boulder, in 1982. He has held faculty positions at the University of Colorado, Boulder, and at the International School for Advanced Studies in Trieste, Italy. Presently he is the Eberly Family Chair Professor of Mathematics at the Pennsylvania State University.
His scientific interests lie mainly in the areas of nonlinear PDEs, control theory and geometric optimization, differential games, and hyperbolic systems of conservation laws.
A. Bressan was a plenary speaker at the International Congress of Mathematicians, Beijing 2002. He received various awards, including
• A. Feltrinelli prize for Mathematics, Mechanics, and Applications, from the Accademia Nazionale dei Lincei in Rome, 2006,
• S.I.A.M. "Analysis of Partial Differential Equations" prize in 2007,
• M. Bôcher prize from the American Mathematical Society in 2008,
• G. Fichera prize from the Unione Matematica Italiana in 2011.
He is member of the Royal Norwegian Society of Sciences and Letters and of the Accademia Nazionale dei Lincei in Rome, and a fellow of the American Mathematical Society. He currently serves on the editorial board of 14 mathematical journals.