Dani Kaufman

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…

hep-th2026

Cluster Algebras, Cube Roots, and Energy Correlators in $N = 4$ SYM

Dani Kaufman, Marcus Spradlin, Anastasia Volovich +1

We provide a cluster algebraic construction of the cube root symbol letters that appear at leading order in the near-collinear expansion of the four-point energy correlator in $\ma…

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.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

Cluster Algebras, Cube Roots, and Energy Correlators in N=4 SYM

Noncommutative Polygonal Cluster Algebras

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

Cluster Algebras, Cube Roots, and Energy Correlators in $N = 4$ SYM

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