Second International Workshop on Differential Algebra and Related Topics

Rutgers University Newark, Newark NJ

Investigators

Abstract

Second International Workshop on Differential Algebra and Related Topics (0724880)} Differential algebra studies differential equations from an algebraic point of view. It extends the analytic study of ordinary and partial differential equations and generalizes the algebraic study of systems of multivariate polynomial equations. Based on the pioneering work of Ritt and foundational and continual research of Kolchin and others throughout much of the last century, differential algebra has evolved into an extremely rich subject. The fields of mathematics with which differential algebra has interactions are highly diversified, ranging from algebraic geometry and mathematical logic to differential equations and Diophantine geometry. More recently, new and improved differential algebraic methods have been incorporated in more and more symbolic computation systems. Since our first international workshop (held at Rutgers University at Newark on November 2--3, 2000), much progress has also been made by researchers in related algebra structures, such as difference algebra, differential schemes, and Rota-Baxter algebra (which has a linear operator that generalizes the integration operator with its integration by parts formula). In particular, the study of Rota-Baxter algebras links several areas of mathematics and physics. This diversity and rapid progress increasingly challenge researchers in one branch of differential algebra to stay ahead of the developments in other branches. Furthermore, the sophistication and specialization of the language make it more difficult for mathematicians in other fields to appreciate the advances in differential algebra. In response to the need raised by the above concerns, we are organizing a second international workshop, to be held again at Rutgers University at Newark in April 12--13, 2007, to bring together international experts from the different branches to give expository talks on their fields. The workshop will provide broad surveys of the methods and results of differential algebra developed since the first workshop, encourage potential collaborations to extend new theories and solve open problems, and attract graduate students and new researchers. To bring the participants further up to date on the most current research results, we are coordinating with organizers of the Kolchin Seminar in Differential Algebra at the City University of New York to hold a Special Session at the AMS meeting at Stevens Institute of Technology immediately following this workshop.