The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes

澳大利亚数学科学界有两个研究小组，他们对应用数学中的Painleve方程非常感兴趣，这些方程能够解决难题。这类问题是为了给出酒井2001年对Painleve方程进行分类的一种最适合应用的形式。为此，我们将与一个看似不同的数学领域建立联系--超几何正交多项式理论中的ASKEY表。该提案建议了一些易于处理的博士项目。

The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - the Askey table from the theory of hypergeometric orthogonal polynomials. A number of tractable PhD projects are suggested by this proposal.