Computational Algebra and its promises for Analysis
Abstract: In this presentation we discuss recent development in the application of computational algebra to the theory of partial differential equations (PDEs). The starting point is the link between PDEs and algebraic properties of certain ideals in R=C[z1,..,zn] or quotient modules, Rm/(A), discovered by Ehrenpreis and Palamodov.
Groebner bases, developed by Bruno Buchberger, make some of the results of Ehrenpreis and Palamodov's effective. We will illustrate these techniques with the Cauchy-Fueter system of several quaternionic variables.
On going research and open problems will be discussed at the end of the presentation.