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.