Title: Finiteness for polynomial functors

Abstract: If a property of tensors, polynomials, or combinations of these is 
preserved under linear coordinate changes and characterisable by polynomial 
equations in the entries of the tensor (or in the coefficients of the polynomial),
then it is in fact characterisable by finitely many such equations. The goal of my
talk is to give a precise meaning to this statement, to show how it comprises
several recent theorems in commutative algebra, and to give an idea about its
proof.