Michel van Garrel, ETH Zürich: BPS invariants of scattering diagrams and spectral networks

Michel van Garrel, ETH Zürich: BPS invariants of scattering diagrams and spectral networks
On one hand, scattering diagrams were developed by Kontsevich-Soibelman and Gross-Siebert in order to smooth Calabi-Yau geometries. On the other hand, one may associate a spectral network to the mirror curve to a toric Calabi-Yau threefold. To the former, one may associate log BPS numbers counting maximally tangent curves. To the latter, one may associate BPS numbers conjecturally counting stable Lagrangians. For a large class of examples for which the toric Calabi-Yau threefolds have no compact divisors, by passing through intermediate quivers, I will show a correspondence between the respective BPS numbers. I will also explain the heuristics behind the correspondence.