Mathematical Sciences: Partial Differential Equations and Moduli of Curves and Bundles

数学科学：偏微分方程以及曲线和丛的模

• 批准号: 9105221
• 负责人: Emma Previato
• 金额: --
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9105221&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Partial; Differential; Equations

The principal investigator will study some problems in algebraic geometry related to partial differential equations. Systems of partial differential equations may be formulated as an integrable system. The solutions of the partial differential equation are realized as integrable manifolds of the system. It is this formulation of systems of partial differential equations which makes the application of methods from algebraic geometry possible. Systems of partial differential equations play an important role in models of physical systems. An important example is in the area of control theory in which one would like to guide an object along a desired trajectory. The system of partial differential equations used to model this situation can be formulated as an integrable system. The research supported by this award should be particularly useful in studying this problem.

首席研究员将研究代数几何中与偏微分方程相关的一些问题。偏微分方程组可以表示为可积系统。偏微分方程的解被实现为系统的可积流形。正是偏微分方程组的这种表述使得代数几何方法的应用成为可能。偏微分方程组在物理系统模型中发挥着重要作用。一个重要的例子是在控制理论领域，人们希望沿着期望的轨迹引导物体。用于模拟这种情况的偏微分方程组可以表示为可积系统。该奖项支持的研究对于研究这个问题应该特别有用。