We study bounds for the Castelnuovoâ€“Mumford regularity of homogeneous ideals in a polynomial ring in terms of the number of variables and the degree of the generators. In particular, our aim is toâ€¦ (More)

This paper introduces a novel compartmental model describing the excretion of 18F-fluoro-deoxyglucose (FDG) in the renal system and a numerical method based on the maximum likelihood for itsâ€¦ (More)

In this paper we show how, given a complex of graded modules and knowing some partial Castelnuovo-Mumford regularities for all the modules in the complex and for all the positive homologies, it isâ€¦ (More)

In this paper we prove that the coordinate ring of the pinched Veronese (i.e k[X, XY, XY , Y , XZ, Y Z, XZ, Y Z, Z] âŠ‚ k[X, Y, Z]) is Koszul. The strategy of the proof is the following: we canâ€¦ (More)

KOSZUL ALGEBRAS, CASTELNUOVO-MUMFORD REGULARITY, AND GENERIC INITIAL IDEALS Giulio Caviglia The University of Kansas Advisor: Craig Huneke August, 2004 The central topics of this dissertation are:â€¦ (More)

For an ideal I in a polynomial ring over a field, a monomial support of I is the set of monomials that appear as terms in a set of minimal generators of I. Craig Huneke asked whether the size of aâ€¦ (More)

A Theorem of Eakin and Sathaye relates the number of generators of a certain power of an ideal with the existence of a distinguished reduction for that ideal. We prove how this result can be obtainedâ€¦ (More)

We show that monomial ideals generated in degree two satisfy a conjecture by Eisenbud, Green and Harris. In particular we give a partial answer to a conjecture of Kalai by proving that h-vectors ofâ€¦ (More)

For a standard graded algebra R, we consider embeddings of the poset of Hilbert functions of R-ideals into the poset of R-ideals, as a way of classification of Hilbert functions. There are examplesâ€¦ (More)