Perturbations of Operator Algebras and Related Topics
算子代数的扰动及相关主题
基本信息
- 批准号:1101403
- 负责人:
- 金额:$ 19.8万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-08-15 至 2015-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project has two main areas of focus. The first of these concerns the perturbation theory of operator algebras with particular reference to the longstanding Kadison-Kastler problem, which asks whether operator algebras that are close in a suitable metric must be isomorphic (or even unitarily equivalent). This is part of a more general and very difficult problem: when two algebras are the same (isomorphic), how can we recognize that this is so? The difficulty arises because the same algebra can have many different, seemingly unrelated, representations. In recent joint work with coauthors, the principal investigator has made considerable progress on the Kadison-Kastler problem, and he plans to continue this work in several directions: an isomorphism result for close crossed product algebras, the K-theory of close algebras, the shared properties of close algebras, and the question of whether close containments lead to embeddings. Recent progress has come for algebras that have the similarity property, and this has a reformulation in cohomological terms. Thus the second main area of focus will be the Kadison-Ringrose problem, which asks whether certain cohomology groups (which act as obstructions to desirable properties) must vanish. This will involve the theory of completely bounded linear and multilinear maps and also connects to the bounded projection property.The modern study of operator algebras has evolved from two main sources. Matrices, which are generalizations of numbers, were introduced to solve equations and now find applications from computer graphics to search engines for the internet. In formulating quantum mechanics mathematically, von Neumann found that he needed infinite-dimensional versions of matrices called linear operators, which were best studied in operator algebras. Moreover, the time-evolution of quantum mechanical systems came to be expressed in terms of the crossed product by groups of automorphisms. The emerging theory of quantum computation is substantially based on the theory of completely bounded and completely positive maps at the matrix level, and these topics underlie much of the work that will be undertaken. Thus, the results obtained in these areas are likely to impact some of these more concrete areas, since the finite factors are those operator algebras that most closely model matrix algebras. An important aspect of the principal investigator's work has been the training of postdoctoral researchers and doctoral students. Most of the young people who have been mentored by the principal investigator are now in faculty positions where they are training the next generation of scientists and engineers. A scientifically and mathematically trained workforce is essential for the technological future of the country, so the principal investigator will continue to give a central role to the mentoring of young mathematicians.
这个项目有两个主要的重点领域。第一个是关于算子代数的微扰理论,特别是长期存在的卡迪逊-卡斯特勒问题,该问题询问在合适度量中接近的算子代数是否必须是同构的(甚至是酉等价的)。这是一个更普遍和更困难的问题的一部分:当两个代数相同(同构)时,我们如何认识到这是如此?困难的出现是因为相同的代数可以有许多不同的,看似不相关的表示。在最近与合著者的合作中,首席研究员在Kadison-Kastler问题上取得了相当大的进展,他计划在几个方向上继续这项工作:紧密交叉积代数的同构结果,紧密代数的k理论,紧密代数的共有性质,以及紧密包含是否导致嵌入的问题。最近的进展是关于具有相似性质的代数,这在上同调项中有一个重新表述。因此,第二个主要关注的领域将是卡迪逊-林罗斯问题,该问题询问某些上同群(作为理想性质的障碍)是否必须消失。这将涉及到完全有界线性和多线性映射的理论,也连接到有界投影性质。算子代数的现代研究有两个主要来源。矩阵是数字的泛化,被用来解方程,现在从计算机图形学到互联网搜索引擎都有应用。在用数学方法表述量子力学时,冯·诺伊曼发现他需要无限维矩阵的线性算子,这在算子代数中得到了最好的研究。此外,量子力学系统的时间演化开始用自同构群的交叉积来表示。新兴的量子计算理论基本上是基于矩阵级的完全有界和完全正映射理论,这些主题是将要进行的大部分工作的基础。因此,在这些领域获得的结果可能会影响一些更具体的领域,因为有限因子是那些最接近模拟矩阵代数的算子代数。首席研究员工作的一个重要方面是培养博士后研究人员和博士生。大多数接受过首席研究员指导的年轻人现在都担任教职,他们正在培训下一代科学家和工程师。一支受过科学和数学训练的劳动力队伍对国家的技术未来至关重要,因此首席研究员将继续在指导年轻数学家方面发挥核心作用。
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 }}
Roger Smith其他文献
HPA axis in the late-gestation ovine fetus? Urocortin: a mechanism for the sustained activation of the
妊娠晚期羊胎儿的 HPA 轴?
- DOI:
- 发表时间:
2016 - 期刊:
- 影响因子:0
- 作者:
J. Challis;A. Holloway;D. Howe;G. Chan;V. Clifton;Roger Smith - 通讯作者:
Roger Smith
Molecular Detection of Methicillin Resistant Staphylococcus Aureus Isolated From Hospital Patients and Food Handlers in FCT , North Central , Nigeria
尼日利亚中北部 FCT 医院患者和食品处理人员分离出的耐甲氧西林金黄色葡萄球菌的分子检测
- DOI:
- 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
M. M. Phillips;K. Krisciunas;N. Suntzeff;R. G. Abraham;M. G. Beckett;M. Bonati;P. Candia;T. Michael Corwin;D. Depoy;J. Espinoza;A. Firth;W. Freedman;G. Galaz;L. Germany;D. González;M. Hamuy;N. C. Hastings;Aimee L. Hungerford;Valentin D. Ivanov;Erika Labbé;R. Marzke;Patrick J. McCarthy;R. McMahon;R. Mcmillan;C. Muena;S. E. Persson;M. Roth;M. T. Ruiz;R. C. Smith;Roger Smith;L. Strolger;Christopher Stubbs - 通讯作者:
Christopher Stubbs
Density functional study of Aun (n = 3–5) clusters on relaxed graphite surfaces
松弛石墨表面上 Aun (n = 3–5) 团簇的密度泛函研究
- DOI:
10.1016/j.susc.2004.11.044 - 发表时间:
2005 - 期刊:
- 影响因子:1.9
- 作者:
G. Wang;J. BelBruno;S. Kenny;Roger Smith - 通讯作者:
Roger Smith
Atrial Natriuretic Peptide, Cyclic GMP Analogues and Modulation of Guanylyl Cyclase do not Alter Stimulated POMC Peptide Release From Perifused Rat or Sheep Corticotrophs
心房钠尿肽、环 GMP 类似物和鸟苷酸环化酶的调节不会改变灌注的大鼠或绵羊促肾上腺皮质激素刺激的 POMC 肽释放
- DOI:
10.1046/j.1365-2826.1997.00665.x - 发表时间:
1997 - 期刊:
- 影响因子:3.2
- 作者:
M. Bowman;P. Robinson;Roger Smith - 通讯作者:
Roger Smith
Roger Smith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('Roger Smith', 18)}}的其他基金
Charge Quantizing CCDs Optimized for Astronomy
针对天文学优化的电荷量化 CCD
- 批准号:
2308380 - 财政年份:2023
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
Prototyping a New Telescope Design for Unprecedented Survey Speed in the Infrared
原型设计新型望远镜,实现前所未有的红外观测速度
- 批准号:
2010041 - 财政年份:2020
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
Modelling radiation resistant low activation High Entropy Alloys
抗辐射低活化高熵合金建模
- 批准号:
EP/S032819/1 - 财政年份:2019
- 资助金额:
$ 19.8万 - 项目类别:
Research Grant
India - UK Civil Nuclear Collaboration: Development of Radiation Damage Resistant High Entropy Alloys for Advanced Nuclear Systems
印度-英国民用核合作:开发用于先进核系统的抗辐射损伤高熵合金
- 批准号:
EP/R021724/1 - 财政年份:2018
- 资助金额:
$ 19.8万 - 项目类别:
Research Grant
Atomistic modelling and experimental verification of vitrified matrices for waste encapsulation
废物封装用玻璃化基质的原子建模和实验验证
- 批准号:
EP/K007882/1 - 财政年份:2013
- 资助金额:
$ 19.8万 - 项目类别:
Research Grant
Intrasynovial soft tissue healing - a novel translational goal for mesenchymal stem cell therapy
滑膜内软组织愈合——间充质干细胞治疗的新转化目标
- 批准号:
MR/J006815/1 - 财政年份:2012
- 资助金额:
$ 19.8万 - 项目类别:
Research Grant
Performance and Reliability of Metallic Materials for Nuclear Fission Power Generation
核裂变发电用金属材料的性能和可靠性
- 批准号:
EP/I003150/1 - 财政年份:2010
- 资助金额:
$ 19.8万 - 项目类别:
Research Grant
Modelling absorption of electromagnetic radiation by carbon-based constituents of the interstellar medium
模拟星际介质碳基成分对电磁辐射的吸收
- 批准号:
EP/F016603/1 - 财政年份:2008
- 资助金额:
$ 19.8万 - 项目类别:
Research Grant
Multiscale modelling and experimental investigation of radiation effects in oxides and heavy metals
氧化物和重金属辐射效应的多尺度建模和实验研究
- 批准号:
EP/F012047/1 - 财政年份:2007
- 资助金额:
$ 19.8万 - 项目类别:
Research Grant
相似海外基金
Operator algebras and index theory in quantum walks and quantum information theory
量子行走和量子信息论中的算子代数和索引论
- 批准号:
24K06756 - 财政年份:2024
- 资助金额:
$ 19.8万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Quantum singularity and non-linear positive maps on operator algebras
算子代数上的量子奇点和非线性正映射
- 批准号:
23K03151 - 财政年份:2023
- 资助金额:
$ 19.8万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Categorical Symmetries of Operator Algebras
算子代数的分类对称性
- 批准号:
2247202 - 财政年份:2023
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
Conference: Groundwork for Operator Algebras Lecture Series 2023
会议:2023 年算子代数系列讲座的基础
- 批准号:
2247796 - 财政年份:2023
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
Conference: East Coast Operator Algebras Symposium 2023
会议:2023 年东海岸算子代数研讨会
- 批准号:
2321632 - 财政年份:2023
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
K-theory of Operator Algebras and Index Theory on Spaces of Singularities
算子代数的K理论与奇点空间索引论
- 批准号:
2247322 - 财政年份:2023
- 资助金额:
$ 19.8万 - 项目类别:
Continuing Grant
New horizons in operator algebras: finite-dimensional approximations and quantized function theory
算子代数的新视野:有限维近似和量化函数理论
- 批准号:
RGPIN-2022-03600 - 财政年份:2022
- 资助金额:
$ 19.8万 - 项目类别:
Discovery Grants Program - Individual
Conference: Groundwork for Operator Algebras Lecture Series (GOALS) 2022
会议:算子代数基础讲座系列 (GOALS) 2022
- 批准号:
2154574 - 财政年份:2022
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
Identities from Vertex Operator Algebras on the Moduli of Curves
曲线模上顶点算子代数的恒等式
- 批准号:
2200862 - 财政年份:2022
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
Operator algebras and operator theory
算子代数和算子理论
- 批准号:
RGPIN-2018-03973 - 财政年份:2022
- 资助金额:
$ 19.8万 - 项目类别:
Discovery Grants Program - Individual