Quantum curves and topological recursion

2015/02/16 by Norbury, Paul
#05A15 #14N10 #81S10 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1502.04394

Abstract

This is a survey article describing the relationship between quantum curves and topological recursion. A quantum curve is a Schrödinger operator-like noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants in a new and interesting way. The Schrödinger 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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