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，在田野研究所（Fields Institute）进行了一个关于几何和拓扑堆栈的研讨会。在这个研讨会上，我们看到了派生的代数几何形状的新兴领域的快照。在一系列出色的演讲中，许多数学家拥有相对较新的博士学位，我们看到了派生方案，派生堆栈，更高类别以及众多几何学和拓扑主体的实施和应用。这个新的研讨会是2007年会议的后续活动：要点是三年后重新访问该领域，以评估发生了什么并查看我们要去的地方。特别是，自2007年以来，派生的代数几何形状及其与较高类别理论领域的相互作用迅速发展，现在是代数拓扑的几个发展中的核心。 这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许多变量中多项式方程系统的解决方案的解决方案。对多项式的重点使所研究的几何对象非常刚性，而拓扑是对现象的研究，在任何连续变形下都保持不变。派生的代数几何形状试图将技术从代数拓扑导入到代数几何形状中，以捕获和计算一些明显被固有的刚性隐藏的更精细的结构。最近取得了惊人的成功。这笔赠款将用于资助美国研究数学家在职业生涯开始之后的出席，以这种方式促进这些思想在更广泛的研究社区中的传播。