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math.QA2023★ 5 cited
Bracelets bases are theta bases
Travis Mandel, Fan Qin
The skein algebra of a marked surface, possibly with punctures, admits the basis of (tagged) bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a cl…
math.QA2016★ 1 cited
Theta bases are atomic
Travis Mandel
Fock and Goncharov conjectured that the indecomposable universally positive (i.e., atomic) elements of a cluster algebra should form a basis for the algebra. This was shown to be f…
math.QA2015★ 11 cited
Scattering diagrams, theta functions, and refined tropical curve counts
Travis Mandel
Working over various graded Lie algebras and in arbitrary dimension, we express scattering diagrams and theta functions in terms of counts of tropical curves/disks, weighted by mul…