Operator algebras and dynamical systems

算子代数和动力系统

基本信息

  • 批准号:
    RGPIN-2018-06855
  • 负责人:
  • 金额:
    $ 1.68万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2018
  • 资助国家:
    加拿大
  • 起止时间:
    2018-01-01 至 2019-12-31
  • 项目状态:
    已结题

项目摘要

In the 1980's, A. Connes introduced non-commutative spaces, and began to develop non-commutative geometry. Today non-commutative geometry a rapidly growing new area of mathematics that contributes to many fields in mathematics and physics. A large source of examples of non-commutative spaces is associated to free minimal actions, up to orbit equivalence, of group of transformations of a topological space. The Bratteli-Vershik model has been a key tool in our study (with I.F. Putnam and C.F. Skau) of topological orbit equivalence of Cantor minimal systems. We plan to extend the Bratteli-Vershik construction to free minimal actions of other groups of homeomorphisms. ******Several properties of von Neumann and C*-algebras translate in properties of their unitary groups. I plan to continue to study and extend such correspondences for both C*-algebras and von Neumann algebras in collaboration with P. W. Ng and with A. Sierakowski. ******One of most important recent development in the theory of C*-algebras is Elliott's classification scheme of amenable C*-algebras. As real C*-algebras and their K-theoretical invariants play an increasingly important role in physics, I plan to enlarge the class of amenable real C*-algebras already classified by their corresponding Elliott's invariant. ******Connes and Woods introduced a new property in ergodic theory called approximate transitivity (AT) to characterize a class of von Neumann algebras. They also noted that the asymptotic boundary of a random walk is AT. I will continue the study of AT and also of the asymptotic boundary of random walks on groups. Then with J. Renault I will analyse the asymptotic boundary of a random walk on a groupoid. Using the notion of dimension spaces, a measure theoretic version of dimension groups, I introduced with D.E. Handelman, we will continue the study of AT(k)_actions, a generalized version of approximate transitivity and of the Poisson boundary of matrix-valued random walks.
20世纪80年代S,A.Connes引入了非交换空间,并开始发展非交换几何。今天,非对易几何是一个迅速发展的数学新领域,对数学和物理的许多领域都有贡献。非对易空间的大量例子与拓扑空间的变换群的自由极小作用有关,直到轨道等价。Bratteli-Vershik模型一直是我们(与I.F.Putnam和C.F.Skau)研究Cantor极小系统拓扑轨道等价性的关键工具。我们计划将Bratteli-Vershik结构推广到自由其他同胚群的极小作用。*von Neumann和C*-代数的几个性质转化为它们的酉群的性质。我计划与P.W.Ng和A.Sierakowski合作,继续研究和推广C*-代数和von Neumann代数的这种对应关系。*C*-代数理论中最重要的发展之一是Elliott关于从属C*-代数的分类方案。随着实C*-代数及其K-理论不变量在物理学中发挥着越来越重要的作用,我计划扩大已由其对应的Elliott不变量分类的可服从实C*-代数的类。*Connes和Wood在遍历理论中引入了一个新的性质,称为近似传递性(AT)来刻画一类von Neumann代数。他们还指出,随机游动的渐近边界是AT。我将继续研究AT以及群上随机游动的渐近边界。然后,我将与J.雷诺一起分析群胚上随机游动的渐近边界。利用维空间的概念,这是我与D.E.Handelman引入的维群的一种测度论版本,我们将继续研究AT(K)_Actions,它是近似传递性的推广版本,以及矩阵值随机游动的Poisson边界。

项目成果

期刊论文数量(0)
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科研奖励数量(0)
会议论文数量(0)
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Giordano, Thierry其他文献

Validating the City Region Food System Approach: Enacting Inclusive, Transformational City Region Food Systems
  • DOI:
    10.3390/su10051680
  • 发表时间:
    2018-05-01
  • 期刊:
  • 影响因子:
    3.9
  • 作者:
    Blay-Palmer, Alison;Santini, Guido;Giordano, Thierry
  • 通讯作者:
    Giordano, Thierry

Giordano, Thierry的其他文献

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{{ truncateString('Giordano, Thierry', 18)}}的其他基金

Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    RGPIN-2018-06855
  • 财政年份:
    2022
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    RGPIN-2018-06855
  • 财政年份:
    2021
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    RGPIN-2018-06855
  • 财政年份:
    2020
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    RGPIN-2018-06855
  • 财政年份:
    2019
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
  • 批准号:
    105463-2012
  • 财政年份:
    2016
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
  • 批准号:
    105463-2012
  • 财政年份:
    2015
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
  • 批准号:
    105463-2012
  • 财政年份:
    2014
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
  • 批准号:
    105463-2012
  • 财政年份:
    2013
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
  • 批准号:
    105463-2012
  • 财政年份:
    2012
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Topological orbit equivalence, amenability, approximate transitivity, antiautomorphisms, unitary groups and operator algebras
拓扑轨道等价、顺应性、近似传递性、反自同构、酉群和算子代数
  • 批准号:
    105463-2007
  • 财政年份:
    2011
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual

相似国自然基金

数学物理中精确可解模型的代数方法
  • 批准号:
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  • 批准年份:
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Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    RGPIN-2018-06855
  • 财政年份:
    2022
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    CRC-2015-00121
  • 财政年份:
    2022
  • 资助金额:
    $ 1.68万
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    Canada Research Chairs
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具有奇点和算子代数的动力系统
  • 批准号:
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  • 财政年份:
    2022
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Operator algebras and dynamical systems
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  • 批准号:
    RGPIN-2018-06855
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  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
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算子代数和动力系统
  • 批准号:
    CRC-2015-00121
  • 财政年份:
    2021
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Canada Research Chairs
Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    RGPIN-2018-06855
  • 财政年份:
    2020
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    CRC-2015-00121
  • 财政年份:
    2020
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Canada Research Chairs
There and back again: operator algebras, algebras and dynamical systems
来来回回:算子代数、代数和动力系统
  • 批准号:
    DP200100155
  • 财政年份:
    2020
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Projects
Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    CRC-2015-00121
  • 财政年份:
    2019
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Canada Research Chairs
Operator algebras and dynamical systems
算子代数和动力系统
  • 批准号:
    RGPIN-2018-06855
  • 财政年份:
    2019
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
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