Mathematical Sciences: Symmetries and Integrability of Difference Equations

小米勒9402625 该奖项涵盖了美国研究数学家参加研讨会的部分费用，该研讨会的主要重点是差分方程的对称性和可积性。 其动机在于努力开发求解非线性微分方程的工具。 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，一个显著的发展例证了可积性理论是引入了逆散射变换。 最近的一个发展是，类似的技术正在成功地应用于解决涉及离散变量的方程：差分方程和微分差分方程。 这种方程在物理学中是重要的，在离散系统的研究和理论上的格子，细胞自动机等，此外，差分方程及其变化已经获得了巨大的突出最近在理论和应用的量子群。 该研讨会汇集了来自美国和加拿大的主要研究人员与相当数量的研究生和博士后教师一起工作，很少有正式的讲座，为期七天，与一些真正令人兴奋的数学和数学物理新兴领域有关的问题。 ***

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. ***