This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4-8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina. The papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 in random matrix theory and also in Mirzakhani's work on the volume of moduli spaces of hyperbolic surfaces. Topological recursion has played a fundamental role in connecting seemingly unrelated areas of mathematics such as matrix models, enumeration of Hurwitz numbers and Grothendieck's dessins d'enfants, Gromov-Witten invariants, the A-polynomials and colored polynomial invariants of knots, WKB analysis, and quantization of Hitchin moduli spaces. In addition to establishing these topics, the volume includes survey papers on the most recent key accomplishments: discovery of the unexpected relation to semi-simple cohomological field theories and a solution to the remodeling conjecture. It also provides a glimpse into the future research direction; for example, connections with the Airy structures, modular functors, Hurwitz-Frobenius manifolds, and ELSV-type formulas.
Chiu-Chu Melissa Liu, Columbia University, New York, NY. Motohico Mulase, University of California, Davis, CA.
J. E. Andersen, G. Borot, and N. Orantin, Modular functors, cohomological field theories, and topological recursion A. Brini, On the Gopakumar-Ooguri-Vafa correspondence for Clifford-Klein 3-manifolds L. Chen, Bouchard-Klemm-Marino-Pasquetti conjecture for $\mathbb{C}^3$ A. Chiodo and J. Nagel, The hybrid Landau-Ginzburg models of Calabi-Yau complete intersections P. Ciosmak, L. Hadasz, M. Manabe, and P. Sulkowski, Singular vector structure of quantum curves N. Do and M. Karev, Towards the topological recursion for double Hurwitz numbers O. Dumitrescu and M. Mulase, Quantization of spectral curves for meromorphic Higgs bundles through topological recursion P. Dunin-Barkowski, Topological recursion and Givental's formalism: Spectral curves for Gromov-Witten theories P. Dunin-Barkowski, P. Norbury, N. Orantin, A. Popolitov, and S. Shadrin, Primary invariants of Hurwitz Frobenius manifolds J. N. Esteves, Hopf algebras and topological recursion B. Fang and Z. Zong, Graph sums in the remodeling conjecture T. Kimura, Double quantization of Seiberg-Witten geometry and W-algebras M. Kontsevich and Y. Soibelman, Airy structures and symplectic geometry of topological recursion D. Korotkin, Periods of meromorphic quadratic differentials and Goldman bracket D. Lewanski, On ELSV-type formulae, Hurwitz numbers and topological recursion X. Liu, M. Mulase, and A. Sorkin, Quantum curves for simple Hurwitz numbers of an arbitrary base curve.
