3 citations · 5 across the 7 of their papers we have counts for
8 papers
The Burer-Monteiro SDP method can fail even above the Barvinok-Pataki bound
Liam O'Carroll, Vaidehi Srinivas, Aravindan Vijayaraghavan
The most widely used technique for solving large-scale semidefinite programs (SDPs) in practice is the non-convex Burer-Monteiro method, which explicitly maintains a low-rank SDP s…
Minimal free resolutions of lattice ideals of digraphs
Liam O'Carroll, Francesc Planas-Vilanova
Based upon a previous work of Manjunath and Sturmfels for a finite, complete, undirected graph, and a refined algorithm by Eröcal, Motsak, Schreyer and Steenpaß for computing syzyg…
On the integral degree of integral ring extensions
José M. Giral, Liam O'Carroll, Francesc Planas-Vilanova +1
Let be an integral ring extension of integral domains with fields of fractions and , respectively. The integral degree of , denoted by ${\rm d}_A(B)…
Non-complete intersection prime ideals in dimension 3
Shiro Goto, Liam O'Carroll, Francesc Planas-Vilanova
We describe prime ideals of height 2 minimally generated by 3 elements in a Gorenstein, Nagata local ring of Krull dimension 3 and multiplicity at most 3. This subject is related t…
Degree and algebraic properties of lattice and matrix ideals
Liam O'Carroll, Francesc Planas-Vilanova, Rafael H. Villarreal
We study the degree of non-homogeneous lattice ideals over arbitrary fields, and give formulae to compute the degree in terms of the torsion of certain factor groups of Z^s and in…
J. Sally's question and a conjecture of Y. Shimoda
Shiro Goto, Liam O'Carroll, Francesc Planas-Vilanova
In 2007, Y. Shimoda, in connection with a long-standing question of J. Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal…
The primary components of positive critical binomial ideals
Liam O'Carroll, Francesc Planas-Vilanova
A natural candidate for a generating set of the (necessarily prime) defining ideal of an -dimensional monomial curve, when the ideal is an almost complete intersection, is a ful…
Ideals of Herzog-Northcott type
Liam O'Carroll, Francesc Planas-Vilanova
This paper takes a new look at ideals generated by 2x2 minors of 2x3 matrices whose entries are powers of three elements not necessarily forming a regular sequence. A special case…