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Quantum curves and topological recursion (1502.04394v1)
Published 16 Feb 2015 in math-ph, math.AG, math.MP, and math.QA
Abstract: This is a survey article describing the relationship between quantum curves and topological recursion. A quantum curve is a Schr\"odinger operator-like noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants in a new and interesting way. The Schr\"odinger operator annihilates a wave function which can be constructed using the WKB method, and conjecturally constructed in a rather different way via topological recursion.
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