Zack Greenberg

A3 exchange complex D4 exchange complex with L3 polylogarithm relation E7 exchange complex E8 exchange complex D4 Affine exchange complex


Email: zgreenberg(AT)mathi(DOT)uni-heidelberg(DOT)de

Research Interests

I study cluster algebras and their applications to a variety of problems including polylogarithm relations and positivity of surface representations.

RTG Lecture Series: Cluster Algebras For Geometers

I am currently giving a lecture series as part of the RTG days at Karsruhe Institute of Technology and Heidelberg University. My lecture notes can be found here: Cluster algebras for Geometers.


Cluster Algebra Explorer

The cluster algebra explorer is a tool I developed to visualize the structure of cluster algebras. The tool allows the user to highlight codimension 1 subalgebras and orbits of A and X coordinates under the cluster modular group.

Cluster Algebra Code

The ocaml library for cluster algebra computations can be found below. It is designed to generate and search cluster complexes and compute cluster modular groups. All the pictures above were generated using this and graphviz/gephi. There is specific support for grassmanian cluster combinatorics, but can work for arbitrary cluster algebras.

Cluster algebra code

Personal Course Notes

My personal notes from class. Hopefully everything is accurate but no guarentees.

Graduate Coursework