Workshop on Stacks in Geometry and Topology

几何和拓扑堆栈研讨会

• 批准号: 0711566
• 负责人: Paul Goerss
• 金额: $ 1.5万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-05-15 至 2008-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0711566&HistoricalAwards=false
• 关键词: Workshop; Stacks; Geometry; Topology

The theory of stacks is the study of symmetries of geometric objects and, assuch, has wide impact throughout mathematics: it is a central theme incurrent work in algebraic geometry, algebraic topology, number theory,analytic and differential geometry, and mathematical physics. Indeed, thetheory has proved flexible enough to apply to any field of mathematics wereit is important to study symmetries across continuous families of geometricobjects, especially when the groups of self-symmetries can varynon-continuously throughout the family. This workshop, to be held at theFields Institute in Toronto, will bring together leading researchers,postdoctoral mathematicians, and graduate students from fields which applythe theory of stacks; the intent is to discuss recent advances, and toexplore and stimulate potentially important new areas of applications. Themain speakers will address current problems in chromatic stable homotopytheory, orbifolds, mathematical physics, geometry in various forms, and theemerging field of derived algebraic geometry. Researchers who have agreed toparticipate include Mark Behrens (MIT), Ian Grojnowksi (Cambridge), JacobLurie (Harvard), Gabriele Vezzosi (Firenze), and Angelo Vistolli (ScuolaNormale Superiore). In addition, Mike Hopkins (Harvard) will give a seriesof lectures concurrently with this workshop.The workshop will be the central event of a two-month subprogramentitled ``Stacks in geometry and topology'', within the thematic program``Geometric applications of homotopy theory''. The full program will runfrom January through June of 2007 at the Fields Institute. Beyond theworkshop, there a directly related mini-courses by Paul Goerss(Northwestern), Ezra Getzler (Northwestern), and Jacob Lurie (Harvard).The workshop and the mini-courses will pursue the theory of stacksacross a diverse fields of mathematics where this theory has been applied,and an important goal of this whole program is to foster cross-disciplinaryinteraction.

堆栈的理论是对几何对象对称性的研究，并且在整个数学过程中都具有广泛的影响：它是代数几何，代数拓扑，数字理论，分析和差异几何学和数学物理学的中心主题始终工作。的确，事实证明，这是足够灵活的，可以应用于任何数学领域，对于研究连续的几何主体家族的对称性很重要，尤其是当自我符号的群体在整个家庭中都可以变化时。 这个研讨会将在多伦多的Thefields研究所举行，将召集领先的研究人员，博士后数学家和来自应用堆栈理论的领域的研究生；目的是讨论最近的进步，并探索和刺激潜在的应用新领域。它们的扬声器将解决色彩稳定同型理论，Orbifolds，数学物理学，各种形式的几何形状以及派生的代数几何形状的呈现领域的当前问题。同意Toparticipate的研究人员包括Mark Behrens（MIT），Ian Grojnowksi（剑桥），Jacoblurie（Harvard），Gabriele Vezzosi（Firenze）和Angelo Vistolli（Scuolanormale Superiore）。 此外，迈克·霍普金斯（Mike Hopkins）（哈佛大学）将与此研讨会同时提供一系列讲座。在主题程序中，该研讨会将是一个为期两个月的子编程``几何和拓扑结构''的核心事件。完整的计划将从1月至2007年6月在Fields Institute举行。除Workshop之外，保罗·盖尔斯（Northwestern），埃兹拉·格茨勒（Ezra Getzler）（西北）和雅各布·卢里（Jacob Lurie）（哈佛大学）直接相关的迷你轮廓。研讨会和迷你巡回赛将追求堆栈群的理论，该理论是该理论的多元化领域，该理论已经应用了一个重要的进度。