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

In: Nankai Symposium on Mathematical Dialogues

Author

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  • Man Wai Mandy Cheung

    (Harvard University)

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.

Suggested Citation

  • Man Wai Mandy Cheung, 2026. "Quantum Cluster Varieties, Scattering Diagrams, and the Deformed Poisson Families," Springer Books, in: Yang-Hui He & Mo-Lin Ge & Cheng-Ming Bai & Jiakang Bao & Edward Hirst (ed.), Nankai Symposium on Mathematical Dialogues, pages 109-117, Springer.
    • Handle: RePEc:spr:sprchp:978-981-19-2328-9_12
    DOI: 10.1007/978-981-19-2328-9_12
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