Resurgent large genus asymptotics of intersection numbers
Factorials can be recursively computed through their definition, but the computation gets difficult quite quickly when the number of interest gets larger and larger. A workaround is given by Stirling’s approximation: a closed, asymptotic formula for factorials. A similar (but much more complicated) situation occurs when trying to compute Witten’s intersection numbers. Virasoro constraints recursively compute these numbers, but the computation gets difficult when the genus gets larger and larger. An approximation has been recently proved by Aggarwal by studying the structure of the associated Virasoro constraints. I will present an alternative proof of Aggarwal’s result based on quantum curves and resurgence. The advantage of this strategy is that it easily generalises to several problems (such as r-spin intersection numbers, Norbury’s intersection numbers, etc) and gives higher-order corrections. Based on the joint work with B. Eynard, E. Garcia-Failde, P. Gregori, and D. Lewański.
- Informed public
- Sergej Monavari
- Laetitia Al-Sulaymaniyin (if you want to attend to the seminar by zoom, please contact me, and I'll give you the link)