FMSP-IPMU special seminar

Speaker: Hayato Chiba (Kyushu university)
Title: Painleve equations and weight system
Date (JST): Mon, Apr 20, 2015, 10:00 - 17:30
Place: Balcony A
Abstract: A weight (a tuple of integers) is one of the invariants of the Painlev\'{e} equation determined by the Newton diagram of the equation. In this talk, several topics about the Painlev\'{e} equations and weights will be introduced.

In the first lecture, a brief review of the Painlev\'{e} equations and the analysis of the Painlev\'{e} equations by means of the weighted projective spaces associated with the weights will be given.

In the second lecture, it will be shown that the weights for the Painlev\'{e} equations are closely related to Saito's theory of weight systems.

In the third lecture, it will be shown that the hierarchy of the Painlev\'{e} equations is obtained from a certain Lie-Poisson structure. The weights are recovered through the Darboux coordinates of the Poisson structure.
Remarks: Break time; 12:00-13:30, 15:00-15:30