| Abstract: |
| This talk surveys recent developments in the relation between skein algebras and quantum cluster algebras for rank-two simple Lie algebras $\mathfrak{g}=\mathfrak{sl}_3,\mathfrak{sp}_4,\mathfrak{g}_2$. I will explain how $\mathfrak{g}$-webs on unpunctured marked surfaces are related to quantum cluster algebras associated with moduli spaces of decorated local systems on the surface. The main goal of the talk is to present the general picture, in particular, how one constructs embeddings of skein algebras into the corresponding quantum cluster algebras. I will also present explicit examples of $\mathfrak{g}$-webs corresponding to cluster variables. |
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