Eynard, B., Orantin, N.: Invariants of algebraic curves and topological expansion. Commun. Number Theory Phys. 1, 347–452 (2007)

Mirzakhani, M.: Simple geodesics and Weil–Petersson volumes of moduli spaces of bordered Riemann surfaces. Invent. Math. 167, 179–222 (2007)

Mirzakhani, M.: Weil–Petersson volumes and intersection theory on the moduli space of curves. J. Am. Math. Soc. 20, 1–23 (2007)

Bouchard, V., Klemm, A., Mariño, M., Pasquetti, S.: Remodeling the B-model. Commun. Math. Phys. 287, 117–178 (2008)

Eynard, B., Mulase, M., Safnuk, B.: The Laplace transform of the cut-and-join equation and the Bouchard–Mariño conjecture on Hurwitz numbers. Publ. Res. Inst. Math. Sci. 47, 629–670 (2011)

Dunin-Barkowski, P., Orantin, N., Shadrin, S., Spitz, L.: Identification of the Givental formula with the spectral curve topological recursion procedure (2012).[arXiv:1211.4021 [physics.math-ph (math.AG, physics.hep-th)]]

Dunin-Barkowski, P., Kazarian, M., Orantin, N., Shadrin, S., Spitz, L.: Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formula (2013). [arXiv:1307.4729 [math.AG (physics.hep-th physics.math-ph)]]

Eynard, B., Orantin, N.: Computation of open Gromov–Witten invariants for toric Calabi–Yau 3-folds by topological recursion, a proof of the BKMP conjecture (2013)

Dumitrescu, O., Mulase, M., Sorkin, A., Safnuk, B.: The spectral curve of the Eynard– Orantin recursion via the Laplace transform. In: Dzhamay, Maruno and Pierce (eds.) Algebraic and Geometric Aspects of Integrable Systems and Random Matrices. Contemporary Mathematics, vol. 593, pp. 263–315 (2013)

[2] Quantum Curves

Dijkgraaf, R., Hollands, L., Sułkowski, P.: Quantum curves and D-modules. J. High Energy Phys. 0810.4157, 1–58 (2009)

Gukov, S., Sułkowski, P.: A-polynomial, B-model, and quantization (2011).[arXiv:1108.0002v1 [hep-th]]

Borot, G., Eynard, B.: All-order asymptotics of hyperbolic knot invariants from non- perturbative topological recursion of A-polynomials (2012).

Dunin-Barkowski, P., Mulase, M., Norbury, P., Popolitov, A., Shadrin, S.: Quantum spectral curve for the Gromov-Witten theory of the complex projective line, [arXiv:1312.5336] (2013)

Dumitrescu, O., Mulase, M.: Quantum curves for Hitchin fibrations and the Eynard-Orantin theory, Letters in Mathematical Physics 104, 635--671 (2014)

[3] Applications and Possible Directions

Fang, B., Liu, C.-C. M., Zong, Z.: All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds, [arXiv:1310.4818 [math.AG]] (2013)

Marian, A., Oprea, D., Pandharipande, R., Pixton, A., Zvonkine, D.: The Chern character of the Verlinde bundle over the moduli space of stable curves, [arXiv:1311.3028] (2013)

Andersen, J.E., Chekhov, L.O., Penner, R.C., Reidys, C.M., Sułkowski, P.: Enumeration of RNA complexes via random matrix theory, [arXiv:1303.1326] (2013)

Borot, G., Eynard, B., Weiße, A.: Root systems, spectral curves, and analysis of a Chern-Simons matrix model for Seifert fibered spaces, [arXiv:1407.4500] (2014)

Nawata, S.: Givental J-functions, Quantum integrable systems, AGT relation with surface operator, [arXiv:1408.4132] (2014)