The Versatility of Integrability

可积系统的思想和方法在许多著名的代数几何、数学物理、概率论和许多其他纯数学和应用数学领域的最新进展中发挥了关键作用。作为一个特别引人注目的例子，我们可以提到krichhever最近对著名的Welters猜想的证明，描述了所有主极化阿贝尔变体中代数曲线的雅可比矩阵。会议将汇集专家和年轻的研究人员，数学家和物理学家，具有不同背景和不同的可积系统的人，讨论在这个非常动态的领域的最新成就。本次会议将于2011年5月4日至7日在纽约哥伦比亚大学举行。如果微分方程的解可以用一个封闭公式给出，而不需要借助于数值或其他近似，则称其为可积方程。近年来，人们发现并分析了许多高度非平凡的可积方程。它们描述了经典（例如某些水波）和现代理论物理中的重要现象，并与纯数学中已知的一些最深的数学结构相联系。在应用数学中，它们构成了对邻近问题的微扰理解的基础，并为数值研究提供了强大的校准工具。本次会议将汇集在可积性的各个方面工作的专家，并将旨在促进我们对可积系统及其在代数，几何和物理中的应用的理解。

Ideas and methods of integrable systems played a key role in many celebrated as well as recent advances in algebraic geometry, mathematical physics, probability, and many other areas of pure and applied mathematics. As a particularly striking example one may mention Krichever's recent proof of the famous Welters' conjecture, characterizing Jacobians of algebraic curves among all principally polarized abelian varieties. The conference will bring together experts and young researchers, mathematicians and physicists, people with different backgrounds and different takes on integrable systems, to discuss the latest achievements in this very dynamic field. This conference will be held at at Columbia University in New York, NY, on May 4-7, 2011.A differential equation is called integrable if its solutions may be given by a closed formula, without a recourse to numerical or other approximations. Many highly nontrivial integrable equations were discovered and analyzed both classically and recently. They describe important phenomena in both classical (e.g. certain water waves) and modern theoretical physics and connect to some of the deepest mathematical structures known in pure mathematics. In applied mathematics, they form a basis of perturbative understanding of nearby problems and give a powerful calibration tool for numerical investigations. This conference will bring together the experts working on various aspects of integrability, and will aim to advance our understanding of integrable systems and their applications in algebra, geometry, and physics.