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.

堆栈理论是对几何对象对称性的研究，因此在整个数学中具有广泛的影响：它是代数几何、代数拓扑、数论、解析几何和微分几何以及数学物理中当前工作的中心主题。事实上，事实证明，该理论足够灵活，可以应用于任何数学领域，因为研究连续几何对象族的对称性很重要，特别是当自对称群可以在整个族中非连续变化时。 该研讨会将在多伦多菲尔兹研究所举行，将汇集堆栈理论应用领域的顶尖研究人员、博士后数学家和研究生；目的是讨论最新进展，探索和激发潜在的重要新应用领域。主要演讲者将讨论色稳定同伦理论、轨道折叠、数学物理、各种形式的几何以及衍生代数几何的新兴领域中的当前问题。同意参与的研究人员包括 Mark Behrens（麻省理工学院）、Ian Grojnowksi（剑桥）、JacobLurie（哈佛大学）、Gabriele Vezzosi（佛罗伦萨）和 Angelo Vistolli（ScuolaNormale Superiore）。 此外，迈克·霍普金斯（哈佛大学）将在本次研讨会的同时进行一系列讲座。本次研讨会将是主题项目“同伦理论的几何应用”内为期两个月的题为“几何和拓扑中的堆栈”的子项目的中心活动。整个项目将于 2007 年 1 月至 6 月在菲尔兹研究所进行。除了研讨会之外，还有 Paul Goerss（西北大学）、Ezra Getzler（西北大学）和 Jacob Lurie（哈佛大学）开设的直接相关的迷你课程。研讨会和迷你课程将在应用该理论的不同数学领域中探讨堆栈理论，整个项目的一个重要目标是促进跨学科互动。