The Versatility of Integrability

可积性的多功能性

• 批准号: 1111152
• 负责人: Andrei Okounkov
• 金额: $ 3万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-03-15 至 2012-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1111152&HistoricalAwards=false
• 关键词: Versatility; Integrability

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.

可积系统的思想和方法在代数几何、数学物理、概率以及纯数学和应用数学的许多其他领域的许多著名和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，人们可以提到克里切弗最近对著名的韦尔特斯猜想的证明，该猜想描述了所有主要极化的阿贝尔变体中代数曲线的雅可比行列式。 会议将汇集专家和年轻研究人员、数学家和物理学家、具有不同背景和对可积系统有不同看法的人们，讨论这个充满活力的领域的最新成就。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由封闭公式给出，而不需要借助数值或其他近似值，则该微分方程称为可积方程。经典和最近发现并分析了许多高度非平凡的可积方程。 它们描述了经典物理学（例如某些水波）和现代理论物理学中的重要现象，并与纯数学中已知的一些最深刻的数学结构联系起来。在应用数学中，它们构成了对附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。这次会议将汇集研究可积性各个方面的专家，旨在增进我们对可积系统及其在代数、几何和物理学中的应用的理解。