Abstract:
I will explain the connection between tropical curves, skein modules, and holomorphic curves in log Calabi—Yau 3-folds. In particular, I will explain a quantum deformation of Mikhalkin’s tropical correspondence formula, and how a quantum torus lie algebra arises when counting closed holomorphic curves in some log Calabi—Yau 3-folds. Apart from some pesky factors of i, this quantum torus lie algebra agrees with the elliptic Hall algebra describing the skein algebra of the thickened torus. In fact, there is a beautiful explicit connection using Ekholm and Shende’s `skeins on branes’ formalism for counting holomorphic curves with boundaries on Lagrangian branes. I will illustrate this through two simple examples, and explain why those pesky factors of i make me think that the worldsheet skein module introduced by Ekholm, Longhi, and Nakamura needs a simple modification to account for some non-local contributions to orientations. The second half of this talk is work in progress.
Language: English
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
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