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的中心主题。事实上，该理论已被证明是灵活的，足以适用于任何数学领域的重要研究对称性跨越连续家庭的geometricobjects，特别是当集团的自对称性可以变化非连续整个家庭。 这个研讨会将在多伦多的菲尔兹研究所举行，将汇集来自应用堆栈理论领域的主要研究人员、博士后数学家和研究生;其目的是讨论最新进展，并探索和激发潜在的重要新应用领域。主要发言者将解决当前的问题，在色稳定同伦理论，orbifolds，数学物理，几何的各种形式，和新兴领域的派生代数几何。同意参加的研究人员包括Mark Behrens（麻省理工学院）、Ian Grojnowksi（剑桥）、JacobLurie（哈佛）、Gabriele Vezzosi（佛罗伦萨）和Angelo Vistolli（Scuola Normale Pastore）。 此外，迈克霍普金斯（哈佛）将给予一系列的讲座同时，这个讲习班将是一个为期两个月的子计划题为"堆栈在几何和拓扑“，在主题计划"几何应用同伦理论”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，还有一个由Paul Goerss（西北大学），Ezra Getzler（西北大学）和Jacob Lurie（哈佛）直接相关的迷你课程。研讨会和迷你课程将在不同的数学领域中追求堆栈理论，这个理论已经应用，整个计划的一个重要目标是促进跨学科的互动。