Pacific Northwest Geometry Seminar

太平洋西北几何研讨会

• 批准号: 0072397
• 负责人: John Lee
• 金额: $ 2.44万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072397&HistoricalAwards=false
• 关键词: Pacific; Northwest; Geometry; Seminar

AbstractAward: DMS-0072397Principal Investigator: John M. LeeThe Pacific Northwest Geometry Seminar for 2000 to 2003 providesopportunities for communication between researchers anddissemination of results and problems in areas such asdifferential geometry, algebraic geometry, mathematical physics,topology, partial differential equations, complex analysis, andgeometric representation theory. Universities based in thenorthwestern United States and British Columbia sponsor thesebiannual conferences, and local participants are augmented byspeakers from outside the region.Modern geometry involves techniques and ideas drawn from all ofmathematics and much of physics. Notions distinctive to thefield include curvature, which deduces from measurements oflength and angle the extent to which a geometric space differsfrom the simplest, flattest models; symplectic structures, whichare the geometric underpinnings for the Hamiltonian formulationof mechanics, and our understanding of their geometry has beenopened up dramatically by ideas borrowed from physics and complexanalysis; and symmetry, since spaces with large groups ofsymmetries often give our best access to algebraic aspects ofthose symmetry groups, and since geometry and analysis at thespace level can yield linear representations of a group orexplain properties of these representations.

摘要奖：DMS-0072397首席研究员：John M.Lee 2000年至2003年的太平洋西北几何研讨会为研究人员之间的交流提供了机会，并传播了在微分几何、代数几何、数学物理、拓扑学、偏微分方程组、复分析和几何表示理论等领域的结果和问题。设在美国西北部和不列颠哥伦比亚省的大学每年主办两次会议，当地与会者还增加了来自该地区以外的演讲者。现代几何涉及从所有数学和大部分物理知识中汲取的技术和思想。该领域特有的概念包括曲率，它从长度和角度的测量中推导出几何空间与最简单、最平的模型的差异程度；辛结构，它是力学的哈密顿公式的几何基础，我们对其几何的理解被借用物理学和复分析的思想极大地打开了；对称性，因为具有大群对称的空间通常是我们获得这些对称群的代数方面的最佳途径，而且因为在空间水平上的几何和分析可以产生一组的线性表示或这些表示的简单性质。