I was a graduate student at the Mas-sachusetts Institute of Technology. The rst three years of these studies were supported by an NSF Graduate Student Fellowship. My research there led to a Ph.D. thesis entitled \Noncommutative ruled surfaces." My thesis research describes certain classes of graded rings which arise as homogeneous coordinate rings of noncommutative quantizations of algebraicall...

Failure to find homogeneous scalar unitary cellular automata (CA) in one dimension led to consideration of only “approximately unitary” CA—which motivated our recent proof of a No-go Lemma in one dimension. In this note we extend the one dimensional result to prove the absence of nontrivial homogeneous scalar unitary CA on Euclidean lattices in any dimension. PACS numbers: 05.30.-d, 89.80.+h, 0...

Let k be an algebraically closed field, let R be an associative kalgebra, and let F = {Mα : α ∈ I} be a family of orthogonal points in Mod(R) such that EndR(Mα) ∼= k for all α ∈ I. Then Mod(F), the minimal full subcategory of Mod(R) which contains F and is closed under extensions, is a full exact Abelian sub-category of Mod(R) and a length category in the sense of Gabriel [8]. In this paper, we...

The phylogenetic relationships between major groups of plesiomorphic pentaradial echinoderms, the Paleozoic crinoids, blastozoans, and edrioasteroids, are poorly understood because of a lack of widely recognized homologies. Here, we present newly recognized oral region homologies, based on the Universal Elemental Homology model for skeletal plates, in a wide range of fossil taxa. The oral regio...

We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given in [Cav04] and [McC]. In particular, we describe a family of three-generated homogeneous ideals in arbitrary characteristic whose projective dimension grows

for every x ∈ X , where ν is a positive real number independent of r,R,R0. Such a triple (X, d,m) will be called a homogeneous space of dimension ν. We point out, however, that a given exponent ν occurring in (1.1) should be considered, more precisely, as an upper bound of the “homogeneous dimension”, hence we should better call (X, d,m) a homogeneous space of dimension less or equal than ν. Ou...