Strong positivity for quantum cluster algebras

Abstract: Quantum cluster algebras are quantizations of cluster algebras, which are a class of algebras interpolating between integrable systems and combinatorics. These algebras were originally introduced to study positivity phenomena arising in the study of quantum groups, and so one of the key questions regarding them (and their quantum analogues) is whether they admit a basis for which the structure constants are positive. The classical version of this question was settled in the affirmative by Gross, Hacking, Keel and Kontsevich. I will present a proof of the quantum version of this positivity for skew-symmetric quantum cluster algebras, due to joint work with Travis Mandel, based on results in categorified Donaldson-Thomas theory and scattering diagrams.

mathematical physicsalgebraic geometrygeometric topologyquantum algebra

Audience: researchers in the discipline

Geometry, Algebra and Physics at KIAS