Thursday, February 20, 2014 - 12:00

427 Thackeray Hall

Mahdi Majidi

CUNY

### Abstract or Additional Information

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.