|
Abstract |
90 min review talk. The theory of discrete Painlevé equations has made great progress in the last two
decades. In this talk, we
first study simple examples of discrete Painlevé equations using their autonomous limits as a clue. Then, after
recapitulating the basic ideas of Sakai's geometric theory of Painlevé equations, we will give an explicit
formulation of the most generic case: the elliptic difference Painlevé equation. Finally, we will derive the
isomonodromic description (Lax formulation) based on the geometric method. If time permits we will also
discuss the tau functions, special solutions, quantization etc. This talk is mainly based on a review with
K.Kajiwara and M.Noumi arXiv:1509.08186. |
