Workshop on Homotopy theory and Derived Algebraic Geometry

同伦理论与派生代数几何研讨会

基本信息

  • 批准号:
    1034873
  • 负责人:
  • 金额:
    $ 2.5万
  • 依托单位:
  • 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

项目摘要

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,在菲尔兹研究所举办了一个关于几何和拓扑堆栈的研讨会;通过这个研讨会,我们看到了派生代数几何这一新兴领域的快照。在一系列引人注目的演讲中,许多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、更高范畴以及随之而来的同伦理论在广泛的几何和拓扑主题中的实施和应用。这一新的研讨会是2007年会议的后续行动:主要观点是三年后再次访问该领域,评估已经发生的情况,并看看我们将走向何方。特别是,派生代数几何及其与更高范畴理论领域的相互作用自2007年以来迅速发展,现在是代数拓扑学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。同意参与的研究人员包括麻省理工学院的Mark Behrens,D-C。Cisinski(巴黎13),Ralph Cohen(Stanford),Andre Henrique(Utrecht),Gerd Laures(Bochum),Tyler Lawson(明尼苏达),Mike Mandell(印第安纳州),Niko Naumann(Regensburg)和Charles Rezk(UIUC)。代数几何是一个经典的数学领域,起源于对多元多项式方程组解的研究。与拓扑学相比,对多项式的关注使所研究的几何对象非常严格,拓扑学是研究在任何连续变形下保持不变的现象。派生的代数几何试图将代数拓扑中的技术引入到代数几何中,以便捕捉和计算一些明显隐藏在固有刚性中的更精细的结构。最近取得了令人瞩目的成功。这笔赠款将用于资助美国研究数学家在职业生涯即将开始时参加会议,以这种方式促进这些想法在更广泛的研究社区中传播。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Paul Goerss其他文献

Realizing unstable injectives
  • DOI:
    10.1007/bf01163658
  • 发表时间:
    1987-06-01
  • 期刊:
  • 影响因子:
    1.000
  • 作者:
    Paul Goerss;Jean Lannes
  • 通讯作者:
    Jean Lannes

Paul Goerss的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Paul Goerss', 18)}}的其他基金

Workshops in Spectral Methods in Algebra, Geometry, and Topology
代数、几何和拓扑谱方法研讨会
  • 批准号:
    2230159
  • 财政年份:
    2022
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Workshops: Homotopy Harnessing Higher Structures
研讨会:利用更高结构的同伦
  • 批准号:
    1833295
  • 财政年份:
    2018
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Conference on Derived Algebraic Geometry
派生代数几何会议
  • 批准号:
    1700795
  • 财政年份:
    2017
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Midwest Topology Seminar
中西部拓扑研讨会
  • 批准号:
    1747457
  • 财政年份:
    2017
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Midwest Topology Seminar, Spring 2014
中西部拓扑研讨会,2014 年春季
  • 批准号:
    1413786
  • 财政年份:
    2014
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Local and Global Chromatic Stable Homotopy Theory
局部和全局色稳定同伦理论
  • 批准号:
    1308916
  • 财政年份:
    2013
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Workshop in Equivariant, Chromatic, and Motivic Homotopy Theory
等变、半音和基元同伦理论研讨会
  • 批准号:
    1261225
  • 财政年份:
    2013
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Chromatic Stable Homotopy Theory and Derived Algebraic Geometry
色稳定同伦理论及其派生代数几何
  • 批准号:
    1007007
  • 财政年份:
    2010
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Continuing Grant
The Topology and Geometry of Topological Field Theories
拓扑场论的拓扑和几何
  • 批准号:
    0852513
  • 财政年份:
    2009
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Workshop on Stacks in Geometry and Topology
几何和拓扑堆栈研讨会
  • 批准号:
    0711566
  • 财政年份:
    2007
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant

相似海外基金

Spheres of Influence: Arithmetic Geometry and Chromatic Homotopy Theory
影响范围:算术几何和色同伦理论
  • 批准号:
    2401472
  • 财政年份:
    2024
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Continuing Grant
A1-Homotopy Theory and Applications to Enumerative Geometry and Number Theory
A1-同伦理论及其在枚举几何和数论中的应用
  • 批准号:
    2405191
  • 财政年份:
    2024
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Stable Homotopy Theory in Algebra, Topology, and Geometry
代数、拓扑和几何中的稳定同伦理论
  • 批准号:
    2414922
  • 财政年份:
    2024
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Computations in Classical and Motivic Stable Homotopy Theory
经典和动机稳定同伦理论的计算
  • 批准号:
    2427220
  • 财政年份:
    2024
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Conference: A Panorama of Homotopy theory
会议:同伦理论全景
  • 批准号:
    2316253
  • 财政年份:
    2023
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Invertibility and deformations in chromatic homotopy theory
色同伦理论中的可逆性和变形
  • 批准号:
    2304797
  • 财政年份:
    2023
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Critical symplectic geometry, Lagrangian cobordisms, and stable homotopy theory
临界辛几何、拉格朗日配边和稳定同伦理论
  • 批准号:
    2305392
  • 财政年份:
    2023
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Conference: Motivic and non-commutative aspects of enumerative geometry, Homotopy theory, K-theory, and trace methods
会议:计数几何的本构和非交换方面、同伦理论、K 理论和迹方法
  • 批准号:
    2328867
  • 财政年份:
    2023
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
Classifying spaces, proper actions and stable homotopy theory
空间分类、适当作用和稳定同伦理论
  • 批准号:
    EP/X038424/1
  • 财政年份:
    2023
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Research Grant
Applications of homotopy theory to algebraic geometry and physics
同伦理论在代数几何和物理学中的应用
  • 批准号:
    2305373
  • 财政年份:
    2023
  • 资助金额:
    $ 2.5万
  • 项目类别:
    Standard Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了