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.
- Pub Date:
- February 2015
- Mathematical Physics;
- Mathematics - Algebraic Geometry;
- Mathematics - Quantum Algebra;
- This article arose out of the Banff workshop Quantum Curves and Quantum Knot Invariants. Comments welcome. 20 pages, 1 figure