FRG: Asymptotic and probabilistic methods in geometric group theory

FRG:几何群论中的渐近和概率方法

基本信息

  • 批准号:
    0455922
  • 负责人:
  • 金额:
    --
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2005
  • 资助国家:
    美国
  • 起止时间:
    2005-06-01 至 2009-05-31
  • 项目状态:
    已结题

项目摘要

The main theme of this project is amenability and related concepts(Kazhdan property T, property tau, unitarizability, etc.) and itsapplications in different areas of mathematics from number theory totopology and functional analysis. In particular, the PIs willconcentrate on the following problems: * Classification of amenable groups and associative algebras, * Amenability of Golod-Shafarevich groups and related problems in3-dimensional topology and number theory, * Expander graphs, property tau for lattices in SL(2,C),probabilistic methods in group theory, * The Dixmier Unitarizability problem, * Constructing new examples of finitely presented groups withproperty T, * Linearity of discrete and pro-p-groups, * Asymptotic properties of discrete groups.The PIs are going to organize several conferences and workshops on differentaspects of the projects. The NSF grant will support several graduatestudents and postdoctoral fellows working undertheir supervision. Group theory was born as the theory of symmetry. The work of Gauss,Abel, Galois, Lie and others showed that groups of symmetries carry essential information about solvability of algebraic anddifferential equations. Group theory plays crucial role in many areas of mathematics and physics. Moreover, recent advances in group theory showed that many areas of mathematics are closely related. In turn, group theory has benefited tremendously from its connections with other areas. About 80 years ago, von Neumann, Banach and Tarski introduced the concept of amenabile group and connected it with basic questions like "Can one assign a weight to any set of points in our space so that the weight is invariant under all symmetries of the space?". The PIs will explore various aspects of amenability of groups and algebras, and deep connections between amenabile groups, number theory and topology.
该项目的主题是可适应性和相关概念(Kazhdan属性T,属性tau,统一性等)。以及它在从数论到拓扑学和泛函分析的不同数学领域中的应用。特别是,PI将集中于以下问题: * 顺从群和结合代数的分类, * Golod-Shafarevich群的顺从性及三维拓扑和数论中的相关问题, * 扩展图,SL(2,C)中格的性质tau,群论中的概率方法, * Dixonitarizability问题, * 构造了具有性质T的群的新例子, * 离散和亲p-基团的线性, * 离散群的渐近性质。PI将组织几次会议和研讨会,讨论项目的不同方面。美国国家科学基金会的拨款将支持一些研究生和博士后研究员在他们的监督下工作。 群论作为对称性理论而诞生。高斯、阿贝尔、伽罗瓦、李和其他人的工作表明,对称群承载着关于代数和微分方程可解性的基本信息。群论在数学和物理的许多领域中起着至关重要的作用。此外,群论的最新进展表明,数学的许多领域是密切相关的。反过来,群论从它与其他领域的联系中受益匪浅。大约80年前,冯·诺依曼,巴拿赫和塔斯基引入了amenabile群的概念,并将其与基本问题联系起来,如“可以给我们空间中的任何点集分配一个权重,使得权重在空间的所有对称性下不变吗?".该PI将探索群体和代数的顺从性的各个方面,以及顺从群体,数论和拓扑学之间的深层联系。

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)

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 }}

Gregory Margulis其他文献

The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant
仿射群的线性部分适当地不连续地作用并留下二次形式不变
  • DOI:
  • 发表时间:
    2011
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Herbert Abels;Gregory Margulis;G. Soifer
  • 通讯作者:
    G. Soifer
Semigroups containing proximal linear maps
包含近端线性映射的半群
  • DOI:
    10.1007/bf02761637
  • 发表时间:
    1995
  • 期刊:
  • 影响因子:
    1
  • 作者:
    Herbert Abels;Gregory Margulis;G. Soifer
  • 通讯作者:
    G. Soifer

Gregory Margulis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('Gregory Margulis', 18)}}的其他基金

Arithmetic, Geometric and Ergodic Aspects of the Theory of Lie Groups and their discrete subgroups
李群及其离散子群理论的算术、几何和遍历方面
  • 批准号:
    1265695
  • 财政年份:
    2013
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Groups: representations and presentations
团体:陈述和演示
  • 批准号:
    0801190
  • 财政年份:
    2008
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Arithmetic, Geometric and Ergodic Aspects of the Theory of Lie groups and their discrete subgroups
李群及其离散子群理论的算术、几何和遍历方面
  • 批准号:
    0801195
  • 财政年份:
    2008
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Arithmetic Groups
算术组
  • 批准号:
    0354731
  • 财政年份:
    2004
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Arithmetic, Geometric and Ergodic Aspects of the Theory of Lie Groups and their Discrete Subgroups
李群及其离散子群理论的算术、几何和遍历方面
  • 批准号:
    0244406
  • 财政年份:
    2003
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Arithmetic, Geometric, and Ergodic Aspects of the Theory of Lie Groups and Their Discrete Subgroups
李群及其离散子群理论的算术、几何和遍历方面
  • 批准号:
    9800607
  • 财政年份:
    1998
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Rigidity of Actions of Higher Rank Lattices
高阶格子作用的刚性
  • 批准号:
    9703770
  • 财政年份:
    1997
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Arithmetic, Geometric and Ergodic Aspects of the Theory of Lie Groups and their Discrete Subgroups
数学科学:李群及其离散子群理论的算术、几何和遍历方面
  • 批准号:
    9424613
  • 财政年份:
    1995
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Arithmetic, Geometric, and Ergodic Aspects of the Theory of Lie Groups and Their Discrete Subgroups
数学科学:李群及其离散子群理论的算术、几何和遍历方面
  • 批准号:
    9204270
  • 财政年份:
    1992
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant

相似海外基金

DMS-EPSRC: Asymptotic Analysis of Online Training Algorithms in Machine Learning: Recurrent, Graphical, and Deep Neural Networks
DMS-EPSRC:机器学习中在线训练算法的渐近分析:循环、图形和深度神经网络
  • 批准号:
    EP/Y029089/1
  • 财政年份:
    2024
  • 资助金额:
    --
  • 项目类别:
    Research Grant
Conference: Geometric and Asymptotic Group Theory with Applications 2024
会议:几何和渐近群理论及其应用 2024
  • 批准号:
    2403833
  • 财政年份:
    2024
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Asymptotic analysis of boundary value problems for strongly inhomogeneous multi-layered elastic plates
强非均匀多层弹性板边值问题的渐近分析
  • 批准号:
    EP/Y021983/1
  • 财政年份:
    2024
  • 资助金额:
    --
  • 项目类别:
    Research Grant
Asymptotic patterns and singular limits in nonlinear evolution problems
非线性演化问题中的渐近模式和奇异极限
  • 批准号:
    EP/Z000394/1
  • 财政年份:
    2024
  • 资助金额:
    --
  • 项目类别:
    Research Grant
Asymptotic behavior of null geodesics near future null infinity and its application
近未来零无穷大零测地线的渐近行为及其应用
  • 批准号:
    22KJ1933
  • 财政年份:
    2023
  • 资助金额:
    --
  • 项目类别:
    Grant-in-Aid for JSPS Fellows
DMS-EPSRC: Asymptotic Analysis of Online Training Algorithms in Machine Learning: Recurrent, Graphical, and Deep Neural Networks
DMS-EPSRC:机器学习中在线训练算法的渐近分析:循环、图形和深度神经网络
  • 批准号:
    2311500
  • 财政年份:
    2023
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Asymptotic theory and infinite-dimensional stochastic calculus
渐近理论和无限维随机微积分
  • 批准号:
    23H03354
  • 财政年份:
    2023
  • 资助金额:
    --
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Asymptotic Analysis of Almost-Periodic Operators of Quantum Mechanics
量子力学准周期算子的渐近分析
  • 批准号:
    2306327
  • 财政年份:
    2023
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Asymptotic analysis of online training algorithms in deep learning
深度学习在线训练算法的渐近分析
  • 批准号:
    2879209
  • 财政年份:
    2023
  • 资助金额:
    --
  • 项目类别:
    Studentship
Asymptotic approximation of the large-scale structure of turbulence in axisymmetric jets: a first principle jet noise prediction method
轴对称射流中湍流大尺度结构的渐近逼近:第一原理射流噪声预测方法
  • 批准号:
    EP/W01498X/1
  • 财政年份:
    2023
  • 资助金额:
    --
  • 项目类别:
    Research Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了