Zachary Greenberg

collaborators

4 papers

math.RT2026

Noncommutative Cluster Varieties and Moduli Spaces of Local Systems

Zachary Greenberg, Dani Kaufman, Merik Niemeyer +1

In this article, we construct noncommutative cluster varieties, $A_{R, S}$ , for each reduced root system $R$ and marked surface $S$ simultaneously generalizing the cluster…

math.RT2024

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-…

math.CO2024

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…

math.RA2024

$SL_{2}$ -like Properties of Matrices Over Noncommutative Rings and Generalizations of Markov Numbers

Zachary Greenberg, Dani Kaufman, Anna Wienhard

We study $2 \times 2$ matrices over noncommutative rings with anti-involution, with a special focus on the symplectic group $Sp_{2} (A, σ)$ . We define traces and dete…

Noncommutative Cluster Varieties and Moduli Spaces of Local Systems

Noncommutative Polygonal Cluster Algebras

Multiplicative Inequalities In Cluster Algebras Of Finite Type

SL2​-like Properties of Matrices Over Noncommutative Rings and Generalizations of Markov Numbers

$SL_{2}$ -like Properties of Matrices Over Noncommutative Rings and Generalizations of Markov Numbers