Higher Airy Structures, $\mathcal {W}$ Algebras and Topological Recursion

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.

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