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. Introduction2. Higher Quantum Airy Structures3. $\mathcal {W}$ algebras and Twisted Modules4. Higher Quantum Airy Structures from $\mathcal {W}$ algebras5. Higher Quantum Airy Structures from Higher Abstract Loop Equations6. $\mathcal {W}$ Constraints and Enumerative GeometryA. Sums over Roots of UnityB. Characterization of Admissible $(r,s)$C. Proof of Uniqueness of the Solution to the Higher Abstract Loop Equations