Deformation/rigidity theory in von Neumann algebras and ergodic theory
冯诺依曼代数中的变形/刚性理论和遍历理论
基本信息
- 批准号:1201565
- 负责人:
- 金额:$ 15.56万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2012
- 资助国家:美国
- 起止时间:2012-06-01 至 2015-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Deformation/rigidity theory, initiated by Sorin Popa in the early 2000's, has been extremely successful over the last decade in answering a number of longstanding problems in von Neumann algebras and ergodic theory. The juxtaposition between deformability properties such as Haagerup's property, free products, or unbounded cocycles, with rigidity properties such as property (T) or spectral gap allows one to discover hidden structure in a von Neumann algebra where both types of phenomena occur. This has led to new insight into the structural properties of these von Neumann algebras, and in turn has found applications to other areas such as measured group theory, or the theory of L2-invariants. The Principal Investigator will continue to investigate and develop these ideas, focusing on their close connection to aspects of ergodic theory. Von Neumann algebras were introduced in the 1930's and 40's in part as a tool for developing a mathematical foundation for quantum physics. Von Neumann algebras have since become a field of independent interest with further applications to areas of mathematics such as ergodic theory, Voiculescu's free probability theory, Jones' theory of subfactors and planar algebras, knot theory, and many others. The development of von Neumann algebras has also historically been closely connected to the study of measurable dynamics and these connections have recently begun to reemerge in the presence of newly developed rigidity phenomenon. The investigation of this rigidity phenomenon has since led to new connections between von Neumann algebras and other areas of mathematics. Furthering the development of rigidity will in turn lead to new insights and connections among these various fields.
变形/刚性理论,索林波帕在21世纪初发起的,已经非常成功地回答了一些长期存在的问题,在冯诺依曼代数和遍历理论在过去的十年。变形性性质(如Haagerup性质、自由乘积或无界上循环)与刚性性质(如性质(T)或谱隙)之间的并列允许人们发现冯诺依曼代数中两种现象都发生的隐藏结构。 这导致了新的洞察力的结构性质,这些冯诺依曼代数,并反过来又发现了应用到其他领域,如测量群论,或理论的L2-不变量。 首席研究员将继续调查和发展这些想法,重点是他们的紧密联系方面的遍历理论。 冯·诺依曼代数是在20世纪30年代和40年代引入的,部分原因是为了发展量子物理学的数学基础。 冯诺依曼代数已成为一个领域的独立利益与进一步应用领域的数学,如遍历理论,Voiculescu的自由概率论,琼斯理论的子因子和平面代数,结理论,和许多其他。 冯·诺依曼代数的发展在历史上也与可测动力学的研究密切相关,这些联系最近开始在新发展的刚性现象中重新出现。 对这种刚性现象的研究导致了冯·诺依曼代数和其他数学领域之间的新联系。 进一步发展刚性反过来又会导致新的见解和这些不同领域之间的联系。
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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Jesse Peterson其他文献
Weighted fusion frame construction via spectral tetris
通过光谱俄罗斯方块构建加权融合框架
- DOI:
- 发表时间:
2012 - 期刊:
- 影响因子:1.7
- 作者:
P. Casazza;Jesse Peterson - 通讯作者:
Jesse Peterson
Some classes of smooth bimodules over IIsub1/sub factors and their associated 1-cohomology spaces
关于 II₁ 型因子上某些光滑双模类及其相关的 1-上同调空间
- DOI:
10.1016/j.jfa.2024.110452 - 发表时间:
2024-08-01 - 期刊:
- 影响因子:1.600
- 作者:
Patrick Hiatt;Jesse Peterson;Sorin Popa - 通讯作者:
Sorin Popa
Group-theoretic constructions of erasure-robust frames
擦除鲁棒框架的群论构造
- DOI:
10.1016/j.laa.2015.04.004 - 发表时间:
2012 - 期刊:
- 影响因子:1.1
- 作者:
M. Fickus;J. Jasper;D. Mixon;Jesse Peterson - 通讯作者:
Jesse Peterson
Hadamard equiangular tight frames
Hadamard 等角紧框架
- DOI:
10.1016/j.acha.2019.08.003 - 发表时间:
2017 - 期刊:
- 影响因子:2.5
- 作者:
M. Fickus;J. Jasper;D. Mixon;Jesse Peterson - 通讯作者:
Jesse Peterson
Polyphase equiangular tight frames and abelian generalized quadrangles
多相等角紧框架和阿贝尔广义四边形
- DOI:
10.1016/j.acha.2017.11.007 - 发表时间:
2016 - 期刊:
- 影响因子:2.5
- 作者:
M. Fickus;J. Jasper;D. Mixon;Jesse Peterson;Cody Watson - 通讯作者:
Cody Watson
Jesse Peterson的其他文献
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{{ truncateString('Jesse Peterson', 18)}}的其他基金
Approximation properties in von Neumann algebras
冯·诺依曼代数中的近似性质
- 批准号:
2400040 - 财政年份:2024
- 资助金额:
$ 15.56万 - 项目类别:
Standard Grant
Annual Spring Institute on Non-Commutative Geometry and Operator Algebra 2020
2020 年春季非交换几何与算子代数研究所
- 批准号:
2000214 - 财政年份:2020
- 资助金额:
$ 15.56万 - 项目类别:
Standard Grant
Rigidity in von Neumann Algebras and Higher Rank Groups
冯·诺依曼代数和高阶群中的刚性
- 批准号:
1801125 - 财政年份:2018
- 资助金额:
$ 15.56万 - 项目类别:
Standard Grant
The 2017 Spring Institute on Noncommutative Geometry and Operator Algebras
2017年春季非交换几何与算子代数学院
- 批准号:
1700457 - 财政年份:2017
- 资助金额:
$ 15.56万 - 项目类别:
Standard Grant
Deformation/rigidity theory in von Neumann algebras and ergodic theory
冯诺依曼代数中的变形/刚性理论和遍历理论
- 批准号:
1500998 - 财政年份:2015
- 资助金额:
$ 15.56万 - 项目类别:
Continuing Grant
Derivations, quantum Dirichlet forms, and deformation/rigidity theory in von Neumann algebras
冯诺依曼代数中的导数、量子狄利克雷形式和变形/刚性理论
- 批准号:
0901510 - 财政年份:2009
- 资助金额:
$ 15.56万 - 项目类别:
Standard Grant
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