Workshop on Homotopy theory and Derived Algebraic Geometry

同伦理论与派生代数几何研讨会

• 批准号: 1034873
• 负责人: Paul Goerss
• 金额: $ 2.5万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-01 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1034873&HistoricalAwards=false
• 关键词: Workshop; Homotopy; theory; Derived; Algebraic

In May 2007 there was a workshop at the Fields Institute on stacks in geometry and topology; with this workshop, we saw a snapshot of the emerging field of derived algebraic geometry. In a remarkable series of talks, many by mathematicians with relatively recent PhDs, we saw the implementation and application of derived schemes, derived stacks, higher categories, and the attendant homotopy theory across a broad spectrum of geometric and topological subjects. This new workshop is a follow-up to the 2007 conference: the main point is to revisit the field three years later, to assess what has happened and to to see where we are going. In particular, the field of derived algebraic geometry and its interplay with higher category theory field has grown rapidly since 2007 and is now central to several developing areas of algebraic topology. It is an ideal moment to explore this interplay. Researchers who have agreed to participate include Mark Behrens (MIT), D-C. Cisinski (Paris 13), Ralph Cohen (Stanford), Andre Henriques (Utrecht), Gerd Laures, (Bochum), Tyler Lawson (Minnesota), Mike Mandell (Indiana), Niko Naumann (Regensburg), and Charles Rezk (UIUC).Algebraic geometry is a classical field of mathematics, arising from the study of solutions of systems of polynomial equations in many variables. The focus on polynomials make the geometric objects studied very rigid, in contrast to topology, which is the study of phenomena which remain unchanged under any continuous deformation. Derived algebraic geometry seeks to import techniques from algebraic topology into algebraic geometry in order to capture and calculate some of the finer structure apparently hidden by the inherent rigidity. There have been remarkable recent successes. This grant will be used to fund the attendance of US research mathematicians near the beginning of their careers, in this way promoting the spread of these ideas among the broader research community.

2007 年 5 月，菲尔兹研究所举办了一场关于几何和拓扑堆栈的研讨会；通过这次研讨会，我们看到了派生代数几何这一新兴领域的概况。在一系列引人注目的演讲中，许多演讲都是由刚刚获得博士学位的数学家主持的，我们看到了派生方案、派生堆栈、更高类别以及随之而来的同伦理论在广泛的几何和拓扑学科中的实施和应用。这个新的研讨会是 2007 年会议的后续活动：主要目的是三年后重新审视该领域，评估已经发生的事情并了解我们的发展方向。特别是，派生代数几何领域及其与更高范畴论领域的相互作用自 2007 年以来迅速发展，目前已成为代数拓扑几个发展领域的核心。 现在是探索这种相互作用的理想时刻。 同意参加的研究人员包括马克·贝伦斯 (Mark Behrens)（麻省理工学院），华盛顿特区。 Cisinski（巴黎 13）、Ralph Cohen（斯坦福）、Andre Henriques（乌得勒支）、Gerd Laures（波鸿）、Tyler Lawson（明尼苏达）、Mike Mandell（印第安纳）、Niko Naumann（雷根斯堡）和 Charles Rezk（UIUC）。代数几何是数学的经典领域，源于该研究 多变量多项式方程组的解。对多项式的关注使得所研究的几何对象变得非常刚性，这与拓扑学不同，拓扑学是研究在任何连续变形下保持不变的现象。派生代数几何试图将代数拓扑的技术引入代数几何，以捕获和计算一些明显隐藏在固有刚性中的更精细的结构。最近取得了显着的成功。这笔赠款将用于资助美国研究数学家在其职业生涯开始时的出席，从而促进这些想法在更广泛的研究界的传播。