Algebraic characterization of autonomy of PDEs

Given an ideal I in the polynomial ring C[x1,...,xn],

the variety V(I) of I is the set of common zeros in C^n

of all the polynomials belonging to I. In algebraic geometry,

one tries to link geometric properties of V(I) with algebraic properties of I.

Analogously, given a system of linear, constant coefficient

partial differential equations, one can consider its zeros, that is,

its solutions in various function and distribution spaces.

One could then hope to link analytic properties of the

set of solutions with algebraic properties of the polynomials

which describe the PDEs.

In this talk, we will focus on one such analytic property,

called autonomy, and we will provide an algebraic characterization

for it.