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.

在2007年5月有一个研讨会在菲尔兹研究所堆栈的几何和拓扑结构;与此研讨会，我们看到了快照的新兴领域派生代数几何。在一系列引人注目的演讲中，许多都是由拥有相对较新的博士学位的数学家所做的，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现和应用。这次新的研讨会是2007年会议的后续行动：主要目的是在三年后重新审视这一领域，评估已经发生的事情，并确定我们的前进方向。特别是，自2007年以来，导出代数几何领域及其与更高范畴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领域的核心。 这是探索这种相互作用的理想时刻。 同意参与的研究人员包括Mark Behrens（MIT），D-C。齐辛斯基（巴黎13），拉尔夫·科恩（斯坦福大学），安德烈·亨里克斯（乌得勒支），格尔德·劳雷斯（波鸿），泰勒·劳森（明尼苏达），迈克·曼德尔（印第安纳州），尼科·瑙曼（里根斯堡）和查尔斯·雷兹克（UIUC）。代数几何是一个经典的数学领域，源于对多变量多项式方程组解的研究。对多项式的关注使得研究的几何对象非常严格，与拓扑学相反，拓扑学研究的是在任何连续变形下保持不变的现象。导出代数几何试图将代数拓扑学中的技术引入代数几何，以捕捉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的出席接近他们的职业生涯的开始，以这种方式促进这些想法在更广泛的研究界的传播。