LisMath Seminar 

21/04/2022, 10:00 — 10:30 — Online
Roberto Vega, Instituto Superior Técnico, Universidade de Lisboa

Resurgent Properties of the Inhomogeneous and "q-deformed'' Painlevé II equations

In this talk we will explore the resurgent properties of the inhomogeneous and "q-deformed'' Painlevé II equations. Both of these equations appear in the double-scaling limit of some matrix models and, in particular, the "q-deformed'' PII describes 2d super-gravity in some special background. After a brief explanation on how resurgent transseries allow us to construct non-perturbative solutions to these equations, we will give some explicit examples of Stokes Data and how they allow us to construct solutions on the whole complex plane. In particular, we will show the computation for the well-known Hastings-McLeod solution and the first one of the special function solutions. We will finish by mentioning the connection between these two equations via the Miura map.