| Abstract: |
| In this talk, I will review the definition of the (reduced) stated ${\rm SL}_n$-skein algebra associated to a punctured bordered surface (or marked surface). I will then introduce a quantum cluster algebra structure on the skew field of fractions of the reduced stated ${\rm SL}_n$-skein algebra in the case where the surface has no interior punctures. Furthermore, I will show that the reduced stated ${\rm SL}_n$-skein algebra embeds into the corresponding quantum cluster algebra when each connected component of the surface contains at least two punctures. In particular, every stated arc is a cluster variable up to multiplication by frozen variables. This is joint work with Min Huang. |
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