We give a brief introduction to (upper) cluster algebras and their
quantization using examples. Then we present several important families
of bases for these algebras using topological models. We also discuss
tropical properties of these bases and their relation to representation
theory.

This article is an extended version of the talk given at the 19th
International Conference on Representations of Algebras (ICRA 2020).

Cluster algebras and their bases

Fan Qin

Abstract