Infinite Discrete Groups
无限离散群
基本信息
- 批准号:1101651
- 负责人:
- 金额:$ 16.14万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-09-01 至 2014-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project has two strands: algebraic versus geometric invariants of groups, and exploring non-positively curved groups. Both fall within the orbit of Gromov's study of infinite discrete groups through large-scale geometry, heavily driven by parallels with Riemannian geometry. The first focuses on filling invariants, which concern the geometric features of discs spanning loops ("soap film geometry") in spaces associated with groups. The second concerns how notions of non-positive curvature in group theory interrelate and the wildness present in non?positively curved groups, particularly in their conjugacy problems and subgroups.The work falls within the subject of Geometric Group Theory, which concerns infinite groups and the spaces on which they act. Its roots lie in the early 20th century, particularly in low-dimensional and algebraic topology. It has taken off since the late 1980s when it became clear that geometric features of the spaces involved have profound repercussions for the algebraic structure of the groups. Rich interactions have ensued with, for example, Riemannian geometry, probability, Lie groups, dynamical systems, ergodic theory, combinatorics, computer science and logic. In addition to the research work, a course in Geometry and Topology will be deigned for undergraduates whose studies who are not primarily concentrated in mathematics.
这个项目有两个方面:代数与几何不变量的群体,并探讨非积极弯曲的群体。两者都属于格罗莫夫通过大尺度几何研究无限离散群的轨道,这在很大程度上是由与黎曼几何的相似之处驱动的。 第一个重点是填充不变量,这涉及到与组相关的空间中的盘跨越环(“肥皂膜几何”)的几何特征。第二个问题是如何在群论中的非正曲率的概念相互关联和野生目前在非?正弯曲群,特别是在他们的共轭问题和子群。工作属于几何群论的主题,其中涉及无限群和空间上,他们的行动福尔斯。它的根源在于世纪早期,特别是在低维和代数拓扑。自20世纪80年代末以来,它已经起飞,当时很明显,所涉及的空间的几何特征对群的代数结构有着深远的影响。丰富的相互作用随之而来,例如,黎曼几何,概率,李群,动力系统,遍历理论,组合数学,计算机科学和逻辑。 除了研究工作,几何和拓扑学课程将被设计为本科生的研究谁不是主要集中在数学。
项目成果
期刊论文数量(0)
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会议论文数量(0)
专利数量(0)
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Timothy Riley其他文献
Active Share and the Predictability of the Performance of Separate Accounts
主动份额和独立账户绩效的可预测性
- DOI:
10.1080/0015198x.2021.1984826 - 发表时间:
2021 - 期刊:
- 影响因子:2.8
- 作者:
M. Cremers;Jon A. Fulkerson;Timothy Riley - 通讯作者:
Timothy Riley
CANNON–THURSTON MAPS DO NOT ALWAYS EXIST
加农-瑟斯顿地图并不总是存在
- DOI:
10.1017/fms.2013.4 - 发表时间:
2012 - 期刊:
- 影响因子:0
- 作者:
Owen Baker;Timothy Riley - 通讯作者:
Timothy Riley
Two Essays on the Low Volatility Anomaly
- DOI:
- 发表时间:
2014 - 期刊:
- 影响因子:3.7
- 作者:
Timothy Riley - 通讯作者:
Timothy Riley
Why Have Actively Managed Bond Funds Remained Popular?
为什么主动管理型债券基金仍然受欢迎?
- DOI:
10.2139/ssrn.3557235 - 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
Jaewon Choi;M. Cremers;Timothy Riley - 通讯作者:
Timothy Riley
Fractional distortion in hyperbolic groups
双曲群中的分数失真
- DOI:
10.1016/j.aim.2025.110418 - 发表时间:
2025-11-01 - 期刊:
- 影响因子:1.500
- 作者:
Pallavi Dani;Timothy Riley - 通讯作者:
Timothy Riley
Timothy Riley的其他文献
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{{ truncateString('Timothy Riley', 18)}}的其他基金
Geometric and Asymptotic Group Theory with Applications 2020
几何和渐近群理论及其应用 2020
- 批准号:
1953998 - 财政年份:2020
- 资助金额:
$ 16.14万 - 项目类别:
Standard Grant
Young Geometric Group Theory Meeting VI
年轻几何群理论会议六
- 批准号:
1660568 - 财政年份:2017
- 资助金额:
$ 16.14万 - 项目类别:
Standard Grant
The geometry, topology and asymptotics of the word problem
文字问题的几何、拓扑和渐进
- 批准号:
0540830 - 财政年份:2005
- 资助金额:
$ 16.14万 - 项目类别:
Standard Grant
The geometry, topology and asymptotics of the word problem
文字问题的几何、拓扑和渐进
- 批准号:
0404767 - 财政年份:2004
- 资助金额:
$ 16.14万 - 项目类别:
Standard Grant
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Geometric quantum representations of discrete groups and their extension to higher category
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Aspects of the coarse geometry of discrete groups
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RGPIN-2019-05172 - 财政年份:2019
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