8 citations · 23 across the 11 of their papers we have counts for
11 papers
Dynamical systems on chain complexes and canonical minimal resolutions
Alexandre Tchernev
We introduce notions of vector field and its (discrete time) flow on a chain complex. The resulting dynamical systems theory provides a set of tools with a broad range of applicabi…
Determinantal hypersurfaces and representations of Coxeter groups
Zeljko Cuckovic, Michael Stessin, Alexandre Tchernev
Given a finite generating set of a group , and a representation of on a Hilbert space , we investigate how the geometry of the set $D(T,ρ)=\{ […
Torsion Freeness of Schur Modules
Muberra Allahverdi, Alexandre Tchernev
Let be a Noetherian commutative ring and an -module with that has rank. Necessary and sufficient conditions were provided by Lebelt for an e…
Betti categories of graded modules and applications to monomial ideals and toric rings
Alexandre Tchernev, Marco Varisco
We introduce the notion of Betti category for graded modules over suitably graded polynomial rings, and more generally for modules over certain small categories. Our categorical ap…
Minimal free resolutions of monomial ideals and of toric rings are supported on posets
Timothy B. P. Clark, Alexandre B. Tchernev
We introduce the notion of a \emph{resolution supported on a poset}. When the poset is a CW-poset, i.e. the face poset of a regular CW-complex, we recover the notion of cellular re…
Spectral algebraic curves and decomposable operator tuples
Michael Stessin, Alexandre Tchernev
Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinanta…