Zack Greenberg

D4 exchange complex with L3 polylogarithm relation

Contact

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.

Papers

Restrictions on Anosov subgroups of Sp(2n,R) with S. Dey and M. Riestenberg
Hopf algebras of multiple polylogarithms, and holomorphic 1-forms with D. Kaufman, H. Li, C. Zickert
The Lie coalgebra of multiple polylogarithms with D. Kaufman, H. Li, C. Zickert
Cluster Modular Groups of Affine and Doubly Extended Cluster Algebras with D. Kaufman.
The following link contains the computational reciepts for the proof of the A-coordinate structure of doubly extended cluster algebras
Thesis: Cluster Algebras and Polylogarithm Relations

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