Pacific Northwest Geometry Seminar

摘要奖：DMS-0072397主要研究者：John M.李太平洋西北几何研讨会为2000年至2003年提供了机会，研究人员之间的沟通和传播的结果和问题，如微分几何，代数几何，数学物理，拓扑学，偏微分方程，复杂的分析，和几何表示理论。 美国西北部和不列颠哥伦比亚省的大学赞助了这些一年两次的会议，当地的参与者也得到了来自该地区以外的演讲者的补充。现代几何学涉及的技术和思想来自所有的数学和大部分物理学。 该领域的独特概念包括曲率，它从长度和角度的测量中推导出几何空间与最简单、最平坦模型的不同程度;辛结构，它是力学的哈密顿公式的几何基础，我们对它们的几何的理解已经被借用物理学和复分析的思想戏剧性地打开了;和对称性，因为具有大群对称性的空间通常使我们能够最好地接触到这些对称群的代数方面，并且因为空间层次上的几何和分析可以产生一个群的线性表示或解释这些表示的性质。

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.