Pacific Northwest Geometry Seminar

2000年至2003年太平洋西北几何研讨会为研究人员提供了交流的机会，并在微分几何、代数几何、数学物理、拓扑学、偏微分方程、复分析和几何表示理论等领域传播结果和问题。总部设在美国西北部和不列颠哥伦比亚省的大学主办了这些两年一次的会议，来自该地区以外的发言者增加了当地与会者的人数。现代几何包含了从所有数学和大部分物理学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断出几何空间与最简单、最平坦的模型的差异程度；辛结构，这是力学哈密顿公式的几何基础，我们对它们几何的理解已经被从物理学和复杂分析中借鉴的思想大大打开了；还有对称性，因为有大量对称的空间通常给我们提供了最好的途径来了解这些对称群的代数方面，因为空间层面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.