Quantum curves and topological recursion
Abstract
This is a survey article describing the relationship between quantum curves and topological recursion. A quantum curve is a Schrödinger operatorlike 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2015
 arXiv:
 arXiv:1502.04394
 Bibcode:
 2015arXiv150204394N
 Keywords:

 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Quantum Algebra;
 14N10;
 05A15;
 81S10
 EPrint:
 This article arose out of the Banff workshop Quantum Curves and Quantum Knot Invariants. Comments welcome. 20 pages, 1 figure