Topological recursion, BPS structures, and quantum curves

Hybrid. https://hu-berlin.zoom.us/j/61686623112 [4]
Contact: Gaetan Borot (borot@hu-berlin.de)
 

Starting from the data of a quadratic (or higher) differential, Gaiotto-Moore-Neitzke's famous study of four-dimensional N=2 supersymmetric QFTs outputs data known as a BPS structure (the same structure describes the output of Donaldson-Thomas theory). To solve a totally different problem in the theory of matrix models, Chekhov and Eynard-Orantin introduced the topological recursion, which takes initial data called a spectral curve and recursively produces (through residue calculus and combinatorics) an infinite tower of geometric invariants, often with an enumerative interpretation.
We will describe recent work connecting these two different theories. In the simplest cases, when the spectral curve is of degree two and genus zero, we describe a simple explicit formula for the “free energies” of the topological recursion purely in terms of a corresponding BPS structure constructed from the same initial data. We will sketch the relation to the WKB analysis of quantum curves, and, time permitting, comment on the "refined" analogue of our constructions. Based on various joint works with K. Iwaki and K. Osuga.