Finite Dimensional Integrable Systems 2015, July 13-17, 2015

该奖项支持美国数学家，特别是那些处于职业生涯早期阶段的数学家，参加2015年7月13日至17日在波兰Bedlewo数学研究和会议中心举行的“有限维可积系统2015”国际会议。有关更多详细信息，请参见http://www.impan.pl/BC/Program/2015.html。 该会议汇集了这一重要且快速发展的研究领域的顶尖专家，沿着还有年轻的数学家和研究生。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。 世纪后半叶，KAM理论及其创始人Kolmogorov、Arnold、Moser的工作为可积性问题的研究提供了新的视角，并推动了这一领域的进一步发展。 新的强大的方法之间的相互作用的基础上的先验断开分支的数学和物理学最近已经开发：方法的复分析，辛和复杂的几何，李理论，表示论，和计算机代数-他们都被用于可积性理论。结果，发现了新的可积系统，发现了可积系统在物理学和几何学中的新应用，发展了研究可积系统的新工具，并回答了许多长期以来悬而未决的问题。会议将调查这一领域的最新进展，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。

This award supports participation of US-based mathematicians, especially those in early career stages, in the international conference "Finite Dimensional Integrable Systems 2015" held at the Mathematical Research and Conference Center in Bedlewo, Poland, on July 13 - 17, 2015. See http://www.impan.pl/BC/Program/2015.html for additional details. The conference brings together leading experts in this important and fast-growing area of research, along with young mathematicians and graduate students.The conference 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.