CBMS Conference: Discrete Painleve Equations

该奖项将资助一个为期5天的会议，该会议将于2016年春季在德克萨斯大学格兰德谷分校举行，主题是离散painlev<s:1>方程。主讲人是澳大利亚悉尼大学的Nalini Joshi教授。painlevel方程的研究与可积系统密切相关，可以用于从大气环流到金属热性能的应用建模。本次会议将特别关注非线性递归关系的解函数，称为离散painlevleve方程。在过去的二十年里，寻找这些方程和研究它们的解已经成为研究的一个主要焦点。然而，人们对它们的一般解所知甚少，主要是因为没有可用的数学工具。讲座将为在研究过程中可能遇到离散painlev<e:1>方程作为模型的数学家和科学家提供信息，并介绍识别和描述非线性非自治差分方程解的数学工具。这次会议将把世界专家Joshi博士带到一个为西班牙裔服务的机构，向不同群体的学生、博士后研究人员和教职员工介绍该领域的新发展。会议发言人将描述离散painlev<e:1>方程的性质，并讨论该领域的巨大新研究进展。主要讲座和补充讲座计划讨论以下主要主题：(1)非线性差分方程的基本理论；(2)离散可积系统与连续可积系统之间的联系；(3)几何与离散painlev<e:1>方程，特别是二阶离散painlev<e:1>方程的联系；(4)离散painlev<e:1>方程的渐近分析；(5)通过Hirota双线性形式和Bäcklund等变换等初等方法求得特解。本次会议由美国国家科学基金会数学科学部基础设施项目和分析项目共同支持。

This award will fund a 5-day conference to be held during the spring of 2016 at the University of Texas Rio Grande Valley on the topic of discrete Painlevé equations. The main lecturer will be Professor Nalini Joshi of the University of Sydney, Australia. The study of Painlevé equations is closely related to integrable systems and can be useful in the modeling of applications from atmospheric circulation to thermal properties of metals. This conference will focus in particular on functions that are solutions of nonlinear recurrence relations, called the discrete Painlevé equations. The search for these equations and study of their solutions has become a major focus of research over the past two decades. However, very little is known about their general solutions, primarily because mathematical tools are not available. The lectures will provide information for mathematicians and scientists who may encounter the discrete Painlevé equations as models in the course of their research and introduce mathematical tools for identifying and describing solutions of nonlinear non-autonomous difference equations. The conference will bring Dr. Joshi, a world-expert, to a Hispanic-serving Institution, introducing new developments in the field to a diverse group of students, postdoctoral researchers, and faculty. The conference speakers will describe the properties of discrete Painlevé equations and discuss tremendous new research developments in the field. The main lectures and the supplemental lectures plan to address the following major themes: (1) the basic theory of nonlinear difference equations; (2) the connection between discrete integrable systems and continuous integrable systems; (3) the connection of geometry with discrete Painlevé equations, especially the ell-discrete Painlevé equation; (4) asymptotic analysis of discrete Painlevé equations; and (5) obtaining special solutions through elementary methods such as Hirota's bilinear form and Bäcklund and other transformations. This conference is jointly supported by the Infrastructure Program and the Analysis Program in the NSF Division of Mathematical Sciences.