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Bracelets are theta functions

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CARW03 - Interdisciplinary applications of cluster algebras

It is known that the bracelets form a basis for the Skein algebra associated with an unpunctured surface. We construct quantum bracelets for quantum cluster algebras arising from the surface possibly with punctures. We further show that the quantum bracelets coincide with the quantum theta functions. Long standing conjectures such as strong positivity and atomicity follow as consequences. This is a joint work with Travis Mandel.

This talk is part of the Isaac Newton Institute Seminar Series series.

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