The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
1. Introduction
2. Higher Quantum Airy Structures
3. $\mathcal {W}$ algebras and Twisted Modules
4. Higher Quantum Airy Structures from $\mathcal {W}$ algebras
5. Higher Quantum Airy Structures from Higher Abstract Loop Equations
6. $\mathcal {W}$ Constraints and Enumerative Geometry
A. Sums over Roots of Unity
B. Characterization of Admissible $(r,s)$
C. Proof of Uniqueness of the Solution to the Higher Abstract Loop Equations
Gaetan Borot, Max Planck Institut fur Mathematik, Bonn, Germany, and Humboldt-Universitat zu Berlin, Germany, Vincent Bouchard, University of Alberta, Edmonton, Alberta, Canada, Nitin K. Chidambaram, University of Alberta, Edmonton, Alberta, Canada, and University of Edinburgh, United Kingdom, Thomas Creutzig, University of Alberta, Edmonton, Alberta, Canada, and Dmitry Noshchenko, University of Warsaw, Poland.
