Mathematical Sciences: Symmetries and Integrability of Difference Equations

9402625米勒该奖项涵盖美国研究数学家参加一个主要关注差分方程式的对称性和可积性的研讨会的部分费用。其动机在于努力开发解决非线性微分方程式的工具。主要有两种方法，一种是李群理论，另一种是可积性理论。在过去的二十年里，证明可积性理论的一个值得注意的发展是逆散射变换的引入。一个更新的发展是，类似的技术正被成功地应用于求解涉及离散变量的方程：差分方程组和微分-差分方程组。这类方程本身在物理、离散系统的研究、晶格理论、元胞自动机等方面都很重要。此外，差分方程及其变体最近在量子群的理论和应用中得到了极大的重视。研讨会汇集了来自美国和加拿大的一批顶尖研究人员，以及相当数量的研究生和博士后教师，在为期七天的时间里，就与一些真正令人兴奋的新兴数学和数学物理领域有关的问题展开合作，几乎没有正式的讲座。***

9402625 Miller This award covers partial expenses for U.S. research mathematicians to participate in a workshop whose primary focus concerns symmetries and integrability of difference equations. The motivation lies in efforts to develop tools for solving nonlinear differential equations. There are two main methods, one involves Lie group theory, the other is integrability theory. A notable development in the last twenty years exemplifying integrability theory was the introduction of the inverse scattering transform. A much more recent development is that similar techniques are being successfully applied to solve equations that involve discrete variables: difference and differential-difference equations. Such equations are important in physics in their own right, in the study of discrete systems and theories on lattices, cellular automata, etc. Moreover, difference equations an variations thereof have gained great prominence recently in the theory and applications of quantum groups. The workshop brings together contingents of leading researchers from the United States and Canada together with a sizable number of graduate students and postdoctoral faculty to work together, with few formal lectures, for a period of seven days on issues related to some of the truly exciting emerging areas of mathematics and mathematical physics. ***