University of Birmingham > Talks@bham > Geometry and Mathematical Physics seminar > Strong positivity for quantum cluster algebras

Strong positivity for quantum cluster algebras

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If you have a question about this talk, please contact Timothy Magee.

I will describe recent joint work with Ben Davison in which we construct “quantum theta bases” for skew-symmetric quantum cluster algebras. These bases satisfy many nice properties; e.g., the structure constants for the multiplication are Laurent polynomials in the quantum parameter with non-negative integer coefficients, thus proving the strong positivity conjecture from quantum cluster theory. Our approach combines structures coming from mirror symmetry (i.e., scattering diagrams and broken lines, as used by Gross-Hacking-Keel-Kontsevich in the classical limit) with results from the DT-theory of quiver representations.

This talk is part of the Geometry and Mathematical Physics seminar series.

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