References
[1] https://www.ams.org/notices/200711/tx071101494p.pdf
[2] https://arxiv.org/pdf/1212.6263.pdf
[3] http://www.maths.dur.ac.uk/users/anna.felikson/talks/cl_alg30min.pdf
[4] https://www.ams.org/journals/bull/2016-53-02/S0273-0979-2015-01514-4/S0273-0979-2015-01514-4.pdf
[5] https://arxiv.org/pdf/1005.1086.pdf
Further Reading on Cluster Algebra
1.) https://en.wikipedia.org/wiki/Cluster_algebra (the "Examples" section is particularly helpful in showcasing cluster algebras' constructions as rings)
2.) http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.235.7230&rep=rep1&type=pdf
3.) https://www.ams.org/notices/200711/tx071101494p.pdf
4.) https://www.msri.org/workshops/595/schedules/15561/documents/1438/assets/16934
Further Reading on Related Topics
1.) http://people.brandeis.edu/~aminul/Docs/ira/ISING/intp+ve.pdf (background on total positivity)
2.) https://sites.math.washington.edu/~morrow/336_12/papers/yuzheng.pdf (introductory Lie Theory)
3.) http://www.maths.liv.ac.uk/TheorPhys/RESEARCH/STRING_THEORY/journal_club/will18Feb2013.pdf (Dynkin Diagrams --- related to cluster algebras of finite type)
