Studies on integrable systems aroud the Painleve systems

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540205
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: The University of Tokyo
• Principal Investigator: SAKAI HIDETAKA 東京大学, 数理(科)学研究科(研究院), 准教授 (50323465)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: パンルヴェ方程式 / 特殊函数 / 差分方程式 / 超幾何函数

Outline of Final Research Achievements

In this research project we have been seeking a higher dimensional analog of theory of the Painleve equations.
In the case of 4-dimension, Kawakami-Nakamura-Sakai had obtained partial classification of the Painleve-type equations. One of the coauthors, Kawakami, is finishing the classification, considering the ramified cases. About another goal of this project, geometrical characterization of the classification, Nakamura, who is another coauthor, took the first step on it. She gave a characterization of the equations by using Namikawa-Ueno's classification of degeneration of genus two curves.
Although Sakai didn't make a big contribution on the development of the theory, our group of research accomplished the initial goals to a respectable degree.

Free Research Field

大域解析学