Alberto Bressan, Distinguished Professor of Mathematics, has been selected to receive the Antonio Feltrinelli Prize in Mathematics, Mechanics, and Applications, which will be awarded in Rome later this fall by the Accademia Nazionale dei Lincei. Founded in 1603, the organization is considered to be Italy's most prestigious scientific society. One of its first members was Galileo Galilei.
The Feltrinelli prize, which includes a monetary grant, a certificate, and a gold medal, is among the highest awards reserved for Italian citizens for achievements in the arts, music, literature, history, philosophy, medicine, and physical and mathematical sciences. "I was thrilled," says Bressan,"to be honored in the same way as some of the people I have admired throughout my life: my favorite writer, Italo Calvino; the music composer Gian Francesco Malipiero; and the movie directors Luchino Visconti, Michelangelo Antonioni, and Ermanno Olmi."
The prize is awarded in the area of physical and mathematical sciences only once every five years. Among the few Italian mathematicians who share this distinction, one can find names that are now part of the history of mathematics, such as Francesco Tricomi, Guido Stampacchia, and the Fields medalist Enrico Bombieri.
Bressan's research interests lie in the broad area of nonlinear analysis, differential equations, and control theory. He is best known for the breakthroughs achieved in the field of hyperbolic conservation laws, where he established the uniqueness and other fundamental properties of solutions, and the convergence of vanishing viscosity approximations. Systems of conservation laws provide the basic mathematical models in continuum physics. For his work on conservation laws, Bressan was invited to deliver a plenary lecture at the International Congress of Mathematicians in Beijing,China, in 2002.
Since joining Penn State, Bressan has gradually shifted his work toward mathematical problems more directly motivated by applications. Applied mathematics is commonly regarded to consist of "filtering down" the knowledge accumulated by centuries of research in pure mathematics -- putting it in a form suitable for diverse applications and developing efficient computational algorithms. However, as Bressan remarks, it is also very important for mathematics itself to receive a constant infusion of new problems and paradigms from other disciplines. "It is the very presence of deep, challenging, open problems that keeps alive the quest for new mathematics, and that can foster the birth of fundamental new ideas," Bressan comments. "For centuries, classical mechanics and continuum physics have provided an extremely rich source of inspiration for mathematicians. In the future, other sciences such as biology, ecology, and economics likely will provide the major impetus for the development of new mathematics."
According to Bressan, working in applied mathematics can be scientifically very rewarding, provided that one carefully selects the problems. For example, he says that his studies of the optimal confinement of forest fires has lead him to an entirely novel class of problems in the calculus of variations. He adds, "Modeling fish harvesting under competitive conditions poses challenging problems in the theory of Nash equilibrium solutions for non-cooperative games, described by elliptic partial differential equations. The optimal management of large queuing networks and supply chains motivates new directions in the theory of conservation laws, where solutions are now defined on a complex network of lines. In all cases, what excites the interest of a mathematician is a problem that requires not just an application of well-established procedures, but also the development of substantially new models and techniques."
Bressan has published a book, titled Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem (published by Oxford University Press in 2000), and more than 130 scientific papers. Prior to joining Penn State in November of 2003, Bressan was a professor at the International School for Advanced Studies (SISSA) in Trieste, Italy, from 1991 to 2003 and an associate professor at the University of Colorado in Boulder from 1986 to 1990. He received his bachelor's degree in mathematics from the University of Padova in Italy in 1978 and his doctoral degree in mathematics from the University of Colorado in Boulder in 1982.
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