# Scattering diagrams, theta functions, and refined tropical curve counts

@article{Mandel2021ScatteringDT, title={Scattering diagrams, theta functions, and refined tropical curve counts}, author={Travis Mandel}, journal={Journal of the London Mathematical Society}, year={2021} }

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 multiplicities given in terms of iterated Lie brackets. Over the tropical vertex group, our tropical curve counts are known to give certain descendant log Gromov-Witten invariants. Working over the quantum torus algebra yields theta functions for quantum cluster varieties, and our tropical description sets up for… Expand

#### 17 Citations

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