3-Manifolds After Perelman; March 2006; Edinburgh, UK

3-佩雷尔曼之后的流形;

基本信息

  • 批准号:
    0601251
  • 负责人:
  • 金额:
    $ 2.2万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2006
  • 资助国家:
    美国
  • 起止时间:
    2006-03-01 至 2007-02-28
  • 项目状态:
    已结题

项目摘要

AbstractAward: DMS-0601251Principal Investigator: Cameron McA. Gordon, Alan W. ReidThe project is a workshop on 3-dimensional topology that will be held atthe International Centre for Mathematical Sciences in Edinburgh, UK, inMarch, 2006. Thurston's Geometrization Conjecture, which has guidedresearch in 3-dimensional topology for almost three decades, has nowbeen established, and consequently there is a need to set out a programfor future research in the subject. This is the objective of theworkshop. The program will be centered around five series of three1-hour lectures, given by Jeff Brock, Dave Gabai, Marc Lackenby, PeterOzsvath, and Peter Shalen. There will also be nine additional invited1-hour talks by other leading researchers. Among the recent importantdevelopments in 3-dimensional topology that will be discussed, with aview to illuminating the theory of 3-manifolds beyond Geometrization,are: the proofs of the Tameness and Ending Lamination Conjectures,Heegaard Floer homology theory, various approaches to the virtual HakenConjecture, and the connection between 3-dimensional topology and thetheory of word hyperbolic groups.3-dimensional topology is a large and active subject within the generalfield of pure mathematics. Its goal is the study of all possible3-dimensional "spaces", and of the various objects that can be situatedin them, such as knots. Over the last 30 years or so this subject hasseen many exciting developments, revealing connections to many otherbranches of mathematics as well as quantum physics and (in the case ofknots) even to the behavior of DNA. The guiding light of the subjectduring this period has been the Geometrization Conjecture, put forwardWilliam Thurston in the mid 1970's, which asserts that hyperbolicgeometry, the non-euclidean geometry discovered by Lobachevsky in the19th century, plays a key role in the description of these 3-dimensionalspaces. This conjecture was recently proved by Grisha Perelman. It seemstimely, then, to take stock of the subject, identifying the majorproblems that remain and indicating potential techniques and directionsfor future work. The core of the program will be five series of three1-hour lectures, given by five internationally renowned experts in thesubject. It is expected that this will make the workshop especiallyuseful to young researchers.The conference web site ishttp://www.icms.org.uk/meetings/2006/3-manifolds/index.html.
摘要奖:DMS-0601251主要研究者:卡梅隆麦卡。作者:Alan W.里德该项目是一个关于三维拓扑的研讨会,将于2006年3月在英国爱丁堡的国际数学科学中心举行。Thurston的几何化猜想在三维拓扑学中的研究已经有了近30年的指导作用,因此有必要为该学科的未来研究制定一个计划。这是研讨会的目的。该计划将围绕五个系列的三个1小时的讲座,由杰夫布罗克,戴夫加拜,马克Lackenby,彼得Ozsvath和彼得沙伦。另外还将邀请其他主要研究人员进行9次1小时的讲座。在最近的重要事态发展,在三维拓扑,将讨论,以期照亮理论的3流形超越几何化,是:Tameness和Ending Lamination猜想的证明,Heegaard Floer同调理论,虚Haken猜想的各种方法,以及三维拓扑与字双曲群理论之间的联系。维拓扑学是纯数学领域中一个庞大而活跃的课题。它的目标是研究所有可能的三维“空间”,以及可以位于其中的各种物体,如结。在过去的30年里,这个学科已经有了许多令人兴奋的发展,揭示了它与许多其他数学分支以及量子物理学的联系,甚至(在结的情况下)与DNA的行为也有联系。在这一时期的主题的指导灯一直是几何化猜想,提出了威廉瑟斯顿在20世纪70年代中期,其中断言,双曲几何,非欧几何发现的罗巴切夫斯基在19世纪世纪,发挥了关键作用,在描述这些三维空间。这个猜想最近被Grisha Perelman证明了。因此,必须对这一主题进行评估,确定仍然存在的主要问题,并指出未来工作的潜在技术和方向。该计划的核心将是五个系列的三个1小时的讲座,由五位国际知名专家在该主题。预计这将使研讨会对年轻的研究人员特别有用。www.icms.org.uk/meetings/2006/3-manifolds/index.html

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)

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Cameron Gordon其他文献

Effect of dung burial by the dung beetle Bubas bison on numbers and viability of Cryptosporidium oocysts in cattle dung.
粪甲虫布巴斯野牛埋粪对牛粪中隐孢子虫卵囊数量和活力的影响。
  • DOI:
    10.1016/j.exppara.2011.06.009
  • 发表时间:
    2011
  • 期刊:
  • 影响因子:
    2.1
  • 作者:
    U. Ryan;Rongchang Yang;Cameron Gordon;B. Doube
  • 通讯作者:
    B. Doube
Harmonic Analysis and Partial Differential Equations
  • DOI:
    10.1007/978-3-031-24311-0
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Cameron Gordon
  • 通讯作者:
    Cameron Gordon
Characterization of a putative Triticum aestivum abscisic acid receptor and its role in fungal pathogen resistance
  • DOI:
  • 发表时间:
    2016-04
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Cameron Gordon
  • 通讯作者:
    Cameron Gordon

Cameron Gordon的其他文献

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{{ truncateString('Cameron Gordon', 18)}}的其他基金

Geometry, Arithmetic, and Groups.
几何、算术和群。
  • 批准号:
    2204684
  • 财政年份:
    2022
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Standard Grant
Characters in Low-Dimensional Topology
低维拓扑中的特征
  • 批准号:
    1830889
  • 财政年份:
    2018
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Standard Grant
Graduate Student Topology and Geometry Conference
研究生拓扑与几何会议
  • 批准号:
    1361929
  • 财政年份:
    2014
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Standard Grant
Conference on low-dimensional topology, knots, and orderable groups
低维拓扑、结和可有序群会议
  • 批准号:
    1305714
  • 财政年份:
    2013
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Standard Grant
Dehn Surgery and Related Topics in 3-Dimensional Topology
Dehn 手术和 3 维拓扑中的相关主题
  • 批准号:
    1309021
  • 财政年份:
    2013
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Standard Grant
Separability and logic in geometric group theory
几何群论中的可分离性和逻辑
  • 批准号:
    0906276
  • 财政年份:
    2009
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Standard Grant
3-dimensional manifolds and related topic
3 维流形及相关主题
  • 批准号:
    0305846
  • 财政年份:
    2003
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Standard Grant
The Topology of Manifolds of Dimensions 3 and 4
3 维和 4 维流形的拓扑
  • 批准号:
    0229035
  • 财政年份:
    2003
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Standard Grant
Spring Topology and Dynamics Conference 2002, at the University of Texas at Austin on March 21-23, 2002
2002 年春季拓扑与动力学会议,2002 年 3 月 21-23 日在德克萨斯大学奥斯汀分校举行
  • 批准号:
    0129227
  • 财政年份:
    2002
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Standard Grant
Low-dimensional Manifolds and Knot Theory
低维流形和纽结理论
  • 批准号:
    9971718
  • 财政年份:
    1999
  • 资助金额:
    $ 2.2万
  • 项目类别:
    Continuing Grant

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