72 citations · 253 across the 16 of their papers we have counts for
21 papers
Poisson geometry and Azumaya loci of cluster algebras
Greg Muller, Bach Nguyen, Kurt Trampel +1
There are two main types of objects in the theory of cluster algebras: the upper cluster algebras with their Gekhtman-Shapiro-Vainshtein Poisson brackets…
Superunitary regions of cluster algebras
Emily Gunawan, Greg Muller
This note introduces the superunitary region of a cluster algebra, the subspace of the totally positive region on which each cluster variable is at least 1. Our main result is that…
Juggler's friezes
Roi Docampo, Greg Muller
This note generalizes -friezes to configurations of numbers in which one of the boundary rows has been replaced by a ragged edge (described by a juggling function).…
Algebraically-Informed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
Mustafa Hajij, Ghada Zamzmi, Matthew Dawson +1
One of the central problems in the interface of deep learning and mathematics is that of building learning systems that can automatically uncover underlying mathematical laws from…
Linear recurrences indexed by
Greg Muller
This note considers linear recurrences (also called linear difference equations) in unknowns indexed by the integers. We characterize a unique \emph{reduced} linear recurrence with…
Non-Commutative Resolutions of Toric Varieties
Eleonore Faber, Greg Muller, Karen E. Smith
Let be the coordinate ring of an affine toric variety. We show that the endomorphism ring where is the (finite) direct sum of all (isomorphism c…
The twist for positroid varieties
Greg Muller, David E Speyer
The purpose of this note is to connect two maps related to certain graphs embedded in the disc. The first is Postnikov's boundary measurement map, which combines partition function…
Lower bound cluster algebras: presentations, Cohen-Macaulayness, and normality
Greg Muller, Jenna Rajchgot, Bradley Zykoski
We give an explicit presentation for each lower bound cluster algebra. Using this presentation, we show that each lower bound algebra Grobner degenerates to the Stanley-Reisner sch…
The greedy basis equals the theta basis
Man Wai Cheung, Mark Gross, Greg Muller +4
We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich.
The existence of a maximal green sequence is not invariant under quiver mutation
Greg Muller
This note provides a quiver which does not admit a maximal green sequence, but which is mutation-equivalent to a quiver which does admit a maximal green sequence. The proof uses th…
Singularities of locally acyclic cluster algebras
Angélica Benito, Greg Muller, Jenna Rajchgot +1
We show that locally acyclic cluster algebras have (at worst) canonical singularities. In fact, we prove that locally acyclic cluster algebras of positive characteristic are strong…
Cluster Algebras of Grassmannians are Locally Acyclic
Greg Muller, David E. Speyer
Considered as commutative algebras, cluster algebras can be very unpleasant objects. However, the first author introduced a condition known as "local acyclicity" which implies that…
A=U for Locally Acyclic Cluster Algebras
Greg Muller
This note presents a self-contained proof that acyclic and locally acyclic cluster algebras coincide with their upper cluster algebras.
Computing upper cluster algebras
Jacob P. Matherne, Greg Muller
This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper…
Skein algebras and cluster algebras of marked surfaces
Greg Muller
This paper defines several algebras associated to an oriented surface with a finite set of marked points on the boundary. The first is the skein algebra , which is spa…
Locally acyclic cluster algebras
Greg Muller
This paper studies cluster algebras locally, by identifying a special class of localizations which are themselves cluster algebras. A `locally acyclic cluster algebra' is a cluster…
Character algebras of decorated SL_2(C)-local systems
Greg Muller, Peter Samuelson
Let S be a path-connected, locally-compact CW-complex, and let M be a subcomplex with finitely-many components. A `decorated SL_2(C)-local system' is an SL_2(C)-local system on S,…
The Weil-Petersson form on an acyclic cluster variety
Greg Muller
The Weil-Petersson form on a cluster variety is a 2-form on a certain open smooth subvariety; the union of the cluster tori. We show that for acyclic cluster varieties, the Weil-Pe…
2D Locus Configurations and the Charged Trigonometric Calogero-Moser System
Greg Muller
A central hyperplane arrangement in C^2 with multiplicity is called a `locus configuration' if it satisfies a series of `locus equations' on each hyperplane. Following Chalykh, Fei…
The Beilinson Equivalence for Differential Operators and Lie Algebroids
Greg Muller
Let D be the ring of differential operators on a smooth irreducible affine variety X over the complex numbers; or, more generally, the enveloping algebra of any locally free Lie al…
Computing a Generating Set of Arithmetic Kleinian Groups
Gregory Muller
The goal of this paper is to demonstrate the use of techniques from hyperbolic geometry to compute generating sets of certain subgroups of ; specifically, $SO^+…