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.

堆栈理论是对几何物体对称性的研究，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、解析和微分几何以及数学物理中当前工作的中心主题。事实上，该理论已被证明足够灵活，可以应用于任何数学领域，因为研究连续几何物体族之间的对称性是很重要的，特别是当自对称组在整个族中可以非连续地变化时。该研讨会将在多伦多菲尔兹研究所举行，将汇集来自应用堆栈理论领域的顶尖研究人员、博士后数学家和研究生；目的是讨论最近的进展，并探索和刺激潜在重要的新应用领域。主讲人将讨论色稳定同伦理论、轨道、数学物理、各种形式的几何以及衍生代数几何的新兴领域的当前问题。同意参与的研究人员包括Mark Behrens（麻省理工学院）、Ian Grojnowksi（剑桥大学）、jacoburie（哈佛大学）、Gabriele Vezzosi（佛罗伦萨大学）和Angelo Vistolli（意大利高等师范学院）。此外，迈克·霍普金斯（哈佛大学）将在研讨会期间进行一系列讲座。该讲习班将是专题方案“同伦理论的几何应用”中一个为期两个月的题为“几何和拓扑中的堆栈”的次级方案的中心活动。整个项目将从2007年1月到6月在菲尔兹研究所进行。在研讨会之外，还有Paul Goerss（西北大学），Ezra Getzler（西北大学）和Jacob Lurie（哈佛大学）直接相关的迷你课程。工作坊和迷你课程将在不同的数学领域探讨堆叠理论，该理论已被应用，整个计划的一个重要目标是促进跨学科的互动。