On a notion of entropy in local algebra

In this talk we will introduce a notion of entropy for certain endomorphisms of Noetherian local rings. We will see how this notion of entropy can be used to extend numerical conditions in Kunz' regularity criterion to all contracting endomorphism of a Noetherian local ring. We will also give an interpretation of the definition of Hilbert-Kunz multiplicity using this notion of entropy. The local ring of an algebraic or analytic variety at a point fixed by a finite self-morphism inherits a local endomorphism whose entropy is well-defined. As an example for this situation we will consider the vertex of the affine cone over a projective variety with a polarized self-morphism and will compare entropy with degree.