2 citations · 2 across the 8 of their papers we have counts for
8 papers
Noncommutative Cluster Varieties and Moduli Spaces of Local Systems
Zachary Greenberg, Dani Kaufman, Merik Niemeyer +1
In this article, we construct noncommutative cluster varieties, , for each reduced root system and marked surface simultaneously generalizing the cluster…
Noncommutative Polygonal Cluster Algebras
Zachary Greenberg, Dani Kaufman, Merik Niemeyer +1
We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein-…
Multiplicative Inequalities In Cluster Algebras Of Finite Type
Michael Gekhtman, Zachary Greenberg, Daniel Soskin
Generalizing the notion of a multiplicative inequality among minors of a totally positive matrix, we describe, over full rank cluster algebras of finite type, the cone of Laurent m…
-like Properties of Matrices Over Noncommutative Rings and Generalizations of Markov Numbers
Zachary Greenberg, Dani Kaufman, Anna Wienhard
We study matrices over noncommutative rings with anti-involution, with a special focus on the symplectic group . We define traces and dete…
Restrictions on Anosov subgroups of Sp(2n,R)
Subhadip Dey, Zachary Greenberg, J. Maxwell Riestenberg
Let and let be a non-empty subset. We prove that if contains an odd integer, then any -Anosov subgroup of ${\rm Sp}(2n,\mathbb{R}…
Hopf algebras of multiple polylogarithms, and holomorphic 1-forms
Zachary Greenberg, Dani Kaufman, Haoran Li +1
We associate to a multiple polylogarithm a holomorphic 1-form on the universal abelian cover of its domain. We relate the 1-forms to the symbol and variation matrix and show that t…
The Lie coalgebra of multiple polylogarithms
Zachary Greenberg, Dani Kaufman, Haoran Li +1
We use Goncharov's coproduct of multiple polylogarithms to define a Lie coalgebra over an arbitrary field. It is generated by symbols subject to inductively defined relations, whic…
Cluster Modular Groups of Affine and Doubly Extended Cluster Algebras
Dani Kaufman, Zachary Greenberg
We calculate the cluster modular groups of affine and doubly extended typecluster algebras in a uniform way by introducing a new family of quivers. We use this uniformdescription t…