Second International Workshop on Differential Algebra and Related Topics

第二届微分代数及相关主题国际研讨会

• 批准号: 0724880
• 负责人: Li Guo
• 金额: $ 0.7万
• 依托单位: Rutgers University Newark
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0724880&HistoricalAwards=false
• 关键词: Second; International; Workshop; Differential; Algebra

Second International Workshop on Differential Algebra and Related Topics (0724880)}Differential algebra studies differential equations from an algebraic point of view. It extends the analytic study of ordinary and partial differential equations and generalizes the algebraic study of systems of multivariate polynomial equations.Based on the pioneering work of Ritt and foundational and continual research of Kolchin and others throughout much of the last century, differential algebra has evolved into an extremely rich subject.The fields of mathematics with which differential algebra has interactions are highly diversified, ranging from algebraic geometry and mathematical logic to differential equations and Diophantine geometry.More recently, new and improved differential algebraic methods have been incorporated in more and more symbolic computation systems. Since our first international workshop (held at Rutgers University at Newark on November 2--3, 2000), much progress has also been made by researchers in related algebra structures, such as difference algebra, differential schemes, and Rota-Baxter algebra (which has a linear operator that generalizes the integration operator with its integration by parts formula). In particular, the study of Rota-Baxter algebras links several areas of mathematics and physics.This diversity and rapid progress increasingly challenge researchers in one branch of differential algebra to stay ahead of the developments in other branches. Furthermore, the sophistication and specialization of the language make it more difficult for mathematicians in other fields to appreciate the advances in differential algebra. In response to the need raised by the above concerns, we are organizing a second international workshop, to be held again at Rutgers University at Newark in April 12--13, 2007, to bring together international experts from the different branches to give expository talks on their fields.The workshop will provide broad surveys of the methods and results of differential algebra developed since the first workshop, encourage potential collaborations to extend new theories and solve open problems, and attract graduate students and new researchers. To bring the participants further up to date on the most current research results, we are coordinating with organizers of the Kolchin Seminar in Differential Algebra at the City University of New York to hold a Special Session at the AMS meeting at Stevens Institute of Technology immediately following this workshop.

第二届国际微分代数及相关主题研讨会（0724880）}微分代数从代数的角度研究微分方程。它扩展了常微分方程和偏微分方程的解析研究，推广了多元多项式方程组的代数研究。基于Ritt的开创性工作以及Kolchin和其他人在上个世纪的大部分时间里的基础和持续研究，微分代数已经发展成为一门极其丰富的学科。与微分代数有相互作用的数学领域是高度多样化的，从代数几何和数学逻辑到微分方程和丢番图几何。最近，新的和改进的微分代数方法已被纳入越来越多的符号计算系统。自从我们的第一次国际研讨会（2000年11月2日至3日在纽瓦克的罗格斯大学举行）以来，研究人员在相关代数结构方面也取得了很大进展，例如差分代数、微分格式和Rota-Baxter代数（它有一个线性算子，它用分部积分公式推广了积分算子）。特别是，Rota-Baxter代数的研究将数学和物理的几个领域联系起来。这种多样性和快速发展日益挑战微分代数一个分支的研究人员保持领先于其他分支的发展。此外，语言的复杂性和专门化使得其他领域的数学家更难理解微分代数的进步。为了回应上述关切所提出的需求，我们正在组织第二次国际研讨会，将于2007年4月12日至13日在纽瓦克的罗格斯大学再次举行，汇集来自不同部门的国际专家，就各自领域进行说明性的演讲。研讨会将提供自第一次研讨会以来发展的微分代数方法和结果的广泛调查，鼓励潜在的合作来扩展新的理论和解决开放的问题，并吸引研究生和新的研究人员。为了让与会者进一步了解最新的研究成果，我们正在与纽约城市大学Kolchin微分代数研讨会的组织者协调，在史蒂文斯理工学院的AMS会议上举行一次特别会议。