Conference: Finite Dimensional Integrable Systems 2022

该项目将支持美国数学家，特别是那些处于职业生涯早期阶段的数学家参加将于2022年6月20日至24日在以色列特拉维夫大学举行的“有限维可积系统2022”国际会议。会议将汇集这一重要且快速发展的研究领域的顶尖专家，以及处于职业生涯早期阶段的数学家和研究生。会议网址是http://www.math.tau.ac.il/~ostrover/Workshop/FDIS2022/FDIS2022.htmlThe，“有限维可积系统2022”，会议的重点是具有有限自由度的可积系统，这是完全可积系统理论中最经典和最流行的部分，可以追溯到拉格朗日，雅可比，科瓦列夫斯卡娅，诺特，庞加莱等人的作品。20世纪下半叶，KAM理论及其创始人（Kolmogorov, Arnold, Moser）的工作为研究可积性问题提供了一个新的视角，并促进了该领域的进一步发展。基于先验的数学和物理分支之间的相互作用，最近发展了新的强大的方法：复分析方法，辛和复几何，李论，表示论和计算机代数-它们都用于可积性理论。结果，发现了新的可积系统，发现了可积系统在物理和几何中的新应用，开发了研究可积系统的新工具，并解答了许多长期悬而未决的问题。会议将调查该领域的最新进展，提出开放的问题，概述新的研究方向，寻找新的应用，并促进新的合作。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The project will support participation of US-based mathematicians, especially those in the early stages of career, in the international conference, "Finite Dimensional Integrable Systems 2022", to be held at the Tel Aviv University, Israel, on June 20-24, 2022. The conference will bring together leading experts in this important and fast growing area of research, along with mathematicians in the early stage of career and graduate students. The conference web site is at http://www.math.tau.ac.il/~ostrover/Workshop/FDIS2022/FDIS2022.htmlThe conference, "Finite Dimensional Integrable Systems 2022", is focused on integrable systems with a finite number of degrees of freedom, the most classical and popular part of the theory of completely integrable systems that goes back to the works of Lagrange, Jacobi, Kovalevskaya, Noether, Poincare and others. In the second half of 20th century, KAM theory and the work of its founders (Kolmogorov, Arnold, Moser) gave a new perspective on integrability problems and stimulated further progress in this area. New powerful methods, based on the interplay between a priori disconnected branches of mathematics and physics, have been recently developed: methods of complex analysis, symplectic and complex geometry, Lie theory, representation theory, and computer algebra - they are all used in the integrability theory. As a result, new integrable systems have been found, new applications of integrable systems in physics and geometry were discovered, new tools for the study of integrable systems were developed and many questions, open for a long time, have been answered. The conference will survey recent progress in this field, present open problems, outline new directions of research, look for new applications, and foster new collaborations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.