Quantum spectral curve

introduction

A quantum curve is a Schrodinger operator-like noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants in a new and interesting way.
One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const.
If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve.
This terminology is prompted by well known results about commuting differential and difference operators, relating pairs of such operators with pairs of meromorphic functions on algebraic curves obeying some conditions.
moduli spaces of quantum curves.
how to quantize a pair of commuting differential or difference operators (i.e. to construct the corresponding quantum curve or discrete quantum curve)
The Schrodinger operator annihilates a wave function which can be constructed using the WKB method, and conjecturally constructed in a rather different way via topological recursion.

http://arxiv.org/abs/1509.06954
Iwaki, Kohei, and Axel Saenz. “Quantum Curve and the First Painlev’e Equation.” arXiv:1507.06557 [math-Ph, Physics:nlin], July 23, 2015. http://arxiv.org/abs/1507.06557.
Zenkevich, Yegor. “Quantum Spectral Curve for (q,t)-Matrix Model.” arXiv:1507.00519 [hep-Th, Physics:math-Ph], July 2, 2015. http://arxiv.org/abs/1507.00519.
Gu, Jie, Albrecht Klemm, Marcos Marino, and Jonas Reuter. ‘Exact Solutions to Quantum Spectral Curves by Topological String Theory’. arXiv:1506.09176 [hep-Th], 30 June 2015. http://arxiv.org/abs/1506.09176.
Gromov, Nikolay, Fedor Levkovich-Maslyuk, and Grigory Sizov. ‘Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4’. arXiv:1504.06640 [hep-Th], 24 April 2015. http://arxiv.org/abs/1504.06640.
Luu, Martin, and Albert Schwarz. ‘Fourier Duality of Quantum Curves’. arXiv:1504.01582 [hep-Th, Physics:math-Ph], 7 April 2015. http://arxiv.org/abs/1504.01582.
Norbury, Paul. ‘Quantum Curves and Topological Recursion’. arXiv:1502.04394 [math-Ph], 15 February 2015. http://arxiv.org/abs/1502.04394.
Gromov, Nikolay, Vladimir Kazakov, Sebastien Leurent, and Dmytro Volin. “Quantum Spectral Curve for Arbitrary State/operator in AdS$_5$/CFT$_4$.” arXiv:1405.4857 [hep-Th, Physics:math-Ph], May 19, 2014. http://arxiv.org/abs/1405.4857.
Schwarz, Albert. ‘Quantum Curves’. arXiv:1401.1574 [hep-Th, Physics:math-Ph], 7 January 2014. http://arxiv.org/abs/1401.1574.