Title: 
Differential Bases and Algebraic Analysis : New Perspectives for Applications

Author: Pommaret, Jean Francois

Affiliation: CERMICS/Ecole Nationale des Ponts et Chaussees
             MARNE-la-VALLEE, FRANCE

Abstract: The purpose of this plenary lecture is to emphasize the use of
Groebner, differential and involutive bases in "algebraic analysis".  This
fashionable though difficult domain of pure mathematics today has been
pioneered by V. P. Palamodov, M. Kashiwara and B. Malgrange around 1970 after
the work of D. C. Spencer on the formal theory of systems of partial
differential equations.  We shall focus on its application to control theory in
order to study linear as well as nonlinear multidimensional control systems by
means of new methods from module theory and homological algebra.  Our
exposition will be rather elementary as we shall insist on the main ideas and
open problems while illustrating the corresponding concepts through explicit
examples.