Quantum Cluster Varieties, Scattering Diagrams, and the Deformed Poisson Families

Man Wai Mandy Cheung ()
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Man Wai Mandy Cheung: Harvard University

A chapter in Nankai Symposium on Mathematical Dialogues, 2026, pp 109-117 from Springer

Abstract: Abstract In this survey article, we discuss the quantum $$\mathcal {A}$$ A and $$\mathcal {X}$$ X cluster varieties and indicate how to relate the two settings. We further state the counter-example to quantum positivity of quantum theta functions. At the end, we illustrate that the quantization of cluster $$\mathcal {X}$$ X varieties can be extended to the deformation families of the $$\mathcal {X}$$ X varieties and their fibers have Poisson structures.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-19-2328-9_12

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DOI: 10.1007/978-981-19-2328-9_12

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