5 papers · 1 filter
Carlsson's Conjecture and the Generalized Total Rank Conjecture in Characteristic Two
Keller VandeBogert
We prove the generalized total rank conjecture over regular rings in characteristic : if is a regular Noetherian domain of characteristic and is a differential -m…
From total positivity to pure free resolutions
Steven V Sam, Keller VandeBogert
Using the Jacobi-Trudi identity as a base, we establish parallels between the theory of totally positive integer sequences and Koszul algebras. We then focus on the case of quadric…
Flagged Perturbations and Anchored Resolutions
Keller VandeBogert
In this paper, we take advantage of a reinterpretation of differential modules admitting a flag structure as a special class of perturbations of complexes. We are thus able to leve…
Ribbon Schur Functors
Keller VandeBogert
We investigate a generalization of the classical notion of a Schur functor associated to a ribbon diagram. These functors are defined with respect to an arbitrary algebra, and in t…
The Total Rank Conjecture in Characteristic Two
Keller VandeBogert, Mark E. Walker
The Total Rank Conjecture is a coarser version of the Buchsbaum-Eisenbud-Horrocks conjecture which, loosely stated, predicts that modules with large annihilators must also have ``l…