7 papers
DG Algebra Structures on Mapping Cones with an Application to Edge Ideals
Hugh Geller, Desiree Martin, Matthew Mastroeni +1
We generalize a construction of Herzog and Takayama pertaining to differential graded algebra structures on mapping cones. Via this generalization, we provide the minimal free reso…
Betti numbers of inductively pierced codes
Hugh Geller, Rebecca R. G., Alexandra Seceleanu +1
Neural ideals were introduced by Curto, Itskov, et al as an algebraic tool to study neural codes. In this paper, we use the notion of polarization introduced by Güntürkün, Jeffries…
DG-Sensitive Pruning & a Complete Classification of DG Trees and Cycles
Hugh Geller, Desiree Martin, Henry Potts-Rubin
Given a squarefree monomial ideal of a polynomial ring , we show that if the minimal free resolution of admits the structure of a differential graded (dg)…
Classifying Betti Numbers of Fiber Products
Ela Celikbas, Hugh Geller, Tony Se
We consider fiber products of complete, local, noetherian algebras over a fixed residue field. Some of these rings cannot be minimally resolved with a free resolution using the rec…
Semidualizing Modules over Numerical Semigroup Rings
Ela Celikbas, Hugh Geller, Toshinori Kobayashi
A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen-Macaulay ring , the ring itself and its canonical module are always realized as…
Canonical forms of neural ideals
Hugh Geller, R. G. Rebecca
Neural ideals, originally defined in arXiv:1212.4201, give a way of translating information about the firing pattern of a set of neurons into a pseudomonomial ideal in a polynomial…
Minimal Free Resolutions of Fiber Products
Hugh Geller
We construct free resolutions for quotient rings , give conditions for the quotient to be realized as a fiber p…