Topological Recursion and Quantum Airy Structures: Titans of Geometry and Physics

• Author / Creator

  Patterson, Devin C.D.

• Topological Recursion began its life as a series of recursive equations aimed at solving constraints which occur in matrix models of Quantum Field Theory. After its inception, Topological Recursion was given a more abstract formulation in terms of Quantum Airy Structures and has since been of help to Gromov-Witten theory, the study of Quantum Curves, enumerative geometry, integrable systems, Hurwitz Theory, and Knot Theory, for example, by revealing a common structure within the solutions to all of these varied problems. We recount the history of Quantum Airy Structures, present the cornerstone theorems upon which their theory depends, and show that these theorems remain true when passing to increasingly broad generalizations. Many of the interesting connections which ignited and maintain engagement with Quantum Airy Structures are put on display.

• Subjects / Keywords

  • Enumerative Geometry
  • Combinatorics
  • Quantum
  • Airy Structures
  • Mathematical Physics

• Graduation date

  Fall 2021

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-xpxv-xg56

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.