Prequels and Possible Sequels to Topological Recursion

Explore a three-part lecture on topological recursion, its historical context, and potential future developments. Begin with a review of the prequel to topological recursion, examining higher Weil-Peterson volumes and logarithmic field theories from the mid-1990s. Delve into the structure of Hopf algebras of graphs, bi-algebras, and Hopf algebras from Feynman categories, focusing on their infinitesimal and logarithmic structures. Conclude by combining these theories, investigating how to obtain moduli spaces from discrete data through cubical complexes, and discussing conjectures about generalizations and future directions in topological recursion.