NSF/CBMS Regional Conference in the Mathematical Sciences: Fully Nonlinear Equations in Geometry

NSF/CBMS 数学科学区域会议：几何中的完全非线性方程

• 批准号: 0225735
• 负责人: Matthew Gursky
• 金额: $ 3.14万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-01-01 至 2003-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0225735&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

The study of nonlinear partial differential equations is necessitated by countless problemsfrom diverse disciplines: physics, economics, biology, etc. Fully nonlinear equations is a more recent subject within this field, but its importance is increasing due to the growing number of connections to other fields. In particular, the study of special Lagrangian submanifolds of Calabi-Yau manifolds is of particular interest in string theory, and consequently an active area of research among physicists and mathematicians alike.Because of the rapid growth and broad interest of the field, it is a natural topic for a CBMS Regional Conference. Researchers and graduate students who are new to the field can see how geometric problems of current interest can be reformulated as problems in nonlinear PDE, and at the same time witness the often surprising ways in which the geometric aspects of the problem inform the analytic aspects (and vice versa).Adding to the appeal of the meeting is the principal lecturer, Prof. Neil Trudinger. His reputation as an eminent researcher and gifted expositor make him an ideal choice to deliver the lectures. Moreover, the monograph resulting from the meeting will be of interest to scientists in a wide range of fields.

来自不同学科的无数问题需要非线性偏微分方程的研究：物理学、经济学、生物学等。全非线性方程是该领域中较新的主题，但由于与其他领域的联系越来越多，其重要性也在增加。 特别是，卡拉比-丘流形的特殊拉格朗日子流形的研究在弦理论中特别令人感兴趣，因此也是物理学家和数学家之间的一个活跃的研究领域。由于该领域的快速发展和广泛的兴趣，它是一个CBMS 区域会议的自然主题。 刚接触该领域的研究人员和研究生可以看到如何将当前感兴趣的几何问题重新表述为非线性偏微分方程中的问题，同时见证问题的几何方面如何影响分析方面的令人惊讶的方式（反之亦然）。首席讲师 Neil Trudinger 教授为会议增添了吸引力。 他作为杰出研究员和天才阐释家的声誉使他成为演讲的理想选择。 此外，会议产生的专着将引起广泛领域的科学家的兴趣。