| Abstract: |
| We begin with a concrete example of Poisson structures associated with the cluster A-algebra from the Markov quiver. Although its Poisson bracket is not log canonical with respect to any cluster seed, it is nevertheless compatible with cluster mutations. We generalize this Poisson structure to the Fock-Goncharov moduli space A_{G,S} associated with punctured surfaces. When G is SL3, we construct a quantization of these Poisson structures, providing a natural generalization of the Roger-Yang Skein algebra. This is joint work in progress with Zhe Sun and Daping Weng. |
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