Quantization of Monodromy data for confluent Painlevé systems, Calabi-Yau 3-algebras and degenerated non-commutative del Pezzo surfaces

Abstract

I shall review relations between the subjects of my title based on my recent work with L. Chekhov and M. Mazzocco (Adv. Math. vol. 376, 2021). I shall describe quantum algebra of functions on affine cubic surfaces naturally appeared as SL₂ «tame» and «wild» character varieties naturally associated with Painlevé confluence. Various quantization schemes and their comparisons will be discussed.