Victor Mishnyakov: Matrix Models, Painlevé Equations, and beta-deformation (from the Painlevé VI point of view)

Abstract

It is a well-known fact that matrix models provide solutions to Painlevé equations. In particular, this is often seen as a consequence of the reduction of certain integrable equations, such as the Toda equations, by the so-called Virasoro constraints—both of which are natural objects in the theory of matrix models. In this paper, I will revisit this scenario in the case of the Painlevé VI equation and its related matrix model, also considering their connection to conformal blocks. Finally, I will explore the possibility of beta-deformations in light of some recent results.