This conference is part of the regional research conference series sponsored by the National Science Foundation (NSF) and the Conference Board of the Mathematical Sciences (CBMS).
The conference will 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 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 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 material is based upon work supported by the National Science Foundation under Grant Number 1543860. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. |