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Title:
The Chromatic Lagrangian and its Quantization
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Abstract:
The chromatic Lagrangian is a Lagrangian subvariety inside a symplectic leaf of the cluster Poisson moduli space of Borel-decorated $PGL(2)$ local systems on a punctured surface. I will describe the cluster quantization of the chromatic Lagrangian, and explain how it canonically determines wavefunctions associated to a certain class of Lagrangian 3-manifolds $L$ in Kahler $\mathbb{C}^3$, equipped with some additional framing data. These wavefunctions are formal power series, which we conjecture encode the all-genus open Gromov-Witten invariants of $L$. Based on joint work with Linhui Shen and Eric Zaslow.
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