Cluster algebras were first introduced by Fomin and Zelevinsky to design an algebraic framework for understanding total positivity and canonical bases for quantum groups. A cluster algebra is a subring of a rational function field generated by a distinguished set of Laurent polynomials called cluster variables. The Positivity Conjecture, which is now a theorem, asserts that the coefficients in any cluster variable are positive. One proof was given by Schiffler and the speaker, and another proof was obtained by Gross, Hacking, Keel and Kontsevich. We outline the idea of our proof.
This video was produced by Syracuse University Department of Mathematics as part of ICRA 2016.
