Quantum Symmetries: Subfactors, Topological Phases, and Higher Categories

量子对称性:子因子、拓扑相和更高类别

基本信息

  • 批准号:
    2154389
  • 负责人:
  • 金额:
    $ 40.27万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2022
  • 资助国家:
    美国
  • 起止时间:
    2022-09-01 至 2025-08-31
  • 项目状态:
    未结题

项目摘要

Symmetry arises in many places in mathematics and the physical sciences. Typically, symmetries of a system are described by the mathematical notion of a group, which is a set with a unit and multiplication, where every operation has an inverse. Groups act on objects by structure-preserving maps. In recent decades, we have seen the emergence of quantum mathematical objects, like von Neumann algebras and topological phases of matter, which naturally live in "higher categories," and so their symmetries are better described by tensor categories. This project aims to study the higher categories arising in the study of von Neumann algebras and topological phases of matter to better understand these quantum systems and their higher quantum symmetries. The project provides research training opportunities for undergraduate and graduate students.This project has three main focuses. First, it continues the investigation of small index subfactors and unitary fusion categories to search for new examples of exotic quantum symmetries. Second, it investigates a nets of operator algebras approach to (2+1)D topological phases of matter, analogous to the conformal net description of conformal field theory. Third, it investigate unitarity for higher categories and its relationship to boundaries and phase transitions for (2+1)D topological phases of matter.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
对称性出现在数学和物理科学的许多地方。通常,系统的对称性由群的数学概念来描述,群是一个具有单位和乘法的集合,其中每个运算都有逆运算。组通过结构保持映射作用于对象。近几十年来,我们已经看到量子数学对象的出现,如冯诺依曼代数和物质的拓扑相,它们自然地生活在“更高的范畴”中,因此它们的对称性可以用张量范畴更好地描述。该项目旨在研究冯诺依曼代数和物质拓扑相研究中出现的更高类别,以更好地理解这些量子系统及其更高的量子对称性。该项目为本科生和研究生提供研究培训机会。首先,它继续研究小指数子因子和幺正融合范畴,以寻找奇异量子对称性的新例子。其次,研究了一种算子代数网对(2+1)维物质拓扑相的描述,类似于共形场论的共形网描述。第三,它调查了更高类别的么正性及其与物质的(2+1)D拓扑相的边界和相变的关系。该奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

期刊论文数量(3)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Composing topological domain walls and anyon mobility
  • DOI:
    10.21468/scipostphys.15.3.076
  • 发表时间:
    2022-08
  • 期刊:
  • 影响因子:
    5.5
  • 作者:
    Peter Huston;F. Burnell;Corey Jones;David Penneys
  • 通讯作者:
    Peter Huston;F. Burnell;Corey Jones;David Penneys
A lattice model for condensation in Levin-Wen systems
  • DOI:
    10.1007/jhep09(2023)055
  • 发表时间:
    2023-03
  • 期刊:
  • 影响因子:
    5.4
  • 作者:
    Jessica M. Christian;David Green;Peter Huston;David Penneys
  • 通讯作者:
    Jessica M. Christian;David Green;Peter Huston;David Penneys
An algebraic quantum field theoretic approach to toric code with gapped boundary
  • DOI:
    10.1063/5.0149891
  • 发表时间:
    2022-12
  • 期刊:
  • 影响因子:
    1.3
  • 作者:
    Daniel Wallick
  • 通讯作者:
    Daniel Wallick
{{ 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 }}

David Penneys其他文献

Subfactors of index exactly 5
指数的子因子恰好为 5
  • DOI:
  • 发表时间:
    2015
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Masaki Izumi;Scott Morrison;David Penneys;Emily Peters;and Noah Snyder
  • 通讯作者:
    and Noah Snyder
CALCULATING TWO-STRAND JELLYFISH RELATIONS
计算两股水母的关系
  • DOI:
    10.2140/pjm.2015.277.463
  • 发表时间:
    2013
  • 期刊:
  • 影响因子:
    0.6
  • 作者:
    David Penneys;E. Peters
  • 通讯作者:
    E. Peters
A Planar Calculus for Infinite Index Subfactors
无限指数子因子的平面微积分
Q-system completion for Csup⁎/sup 2-categories
Csup⁎/sup 2-范畴的 Q 系统完备性
  • DOI:
    10.1016/j.jfa.2022.109524
  • 发表时间:
    2022-08-01
  • 期刊:
  • 影响因子:
    1.600
  • 作者:
    Quan Chen;Roberto Hernández Palomares;Corey Jones;David Penneys
  • 通讯作者:
    David Penneys
1-Supertransitive Subfactors with Index at Most $${6\frac{1}{5}}$$
  • DOI:
    10.1007/s00220-014-2160-4
  • 发表时间:
    2014-09-18
  • 期刊:
  • 影响因子:
    2.600
  • 作者:
    Zhengwei Liu;Scott Morrison;David Penneys
  • 通讯作者:
    David Penneys

David Penneys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('David Penneys', 18)}}的其他基金

Conference: 2023 Great Plains Operator Theory Symposium
会议:2023年大平原算子理论研讨会
  • 批准号:
    2247732
  • 财政年份:
    2023
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Standard Grant
2019 East Coast Operator Algebra Symposium
2019东海岸算子代数研讨会
  • 批准号:
    1936283
  • 财政年份:
    2019
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Standard Grant
CAREER: Representing and Classifying Enriched Quantum Symmetry
职业:丰富的量子对称性的表示和分类
  • 批准号:
    1654159
  • 财政年份:
    2017
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Continuing Grant
Classifying subfactors and fusion categories
对子因素和融合类别进行分类
  • 批准号:
    1655912
  • 财政年份:
    2016
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Standard Grant
Classifying subfactors and fusion categories
对子因素和融合类别进行分类
  • 批准号:
    1500387
  • 财政年份:
    2015
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Standard Grant
EAPSI: Multicolored Planar Algebras and Quadrilaterals of Subfactors
EAPSI:多彩平面代数和子因子四边形
  • 批准号:
    1015571
  • 财政年份:
    2010
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Fellowship Award

相似海外基金

REU Site: Research in Symmetries at the University of Kentucky
REU 网站:肯塔基大学对称性研究
  • 批准号:
    2349261
  • 财政年份:
    2024
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Continuing Grant
Geometric evolution of spaces with symmetries
具有对称性的空间的几何演化
  • 批准号:
    DP240101772
  • 财政年份:
    2024
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Discovery Projects
Lagrangian Multiforms for Symmetries and Integrability: Classification, Geometry, and Applications
对称性和可积性的拉格朗日多重形式:分类、几何和应用
  • 批准号:
    EP/Y006712/1
  • 财政年份:
    2024
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Fellowship
CAREER: Symmetries and Classical Physics in Machine Learning for Science and Engineering
职业:科学与工程机器学习中的对称性和经典物理学
  • 批准号:
    2339682
  • 财政年份:
    2024
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Continuing Grant
Canonical Singularities, Generalized Symmetries, and 5d Superconformal Field Theories
正则奇点、广义对称性和 5d 超共形场论
  • 批准号:
    EP/X01276X/1
  • 财政年份:
    2023
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Fellowship
Characterization of Systematic Effects in Ultracold Neutron Tests of Fundamental Symmetries
基本对称性超冷中子测试中系统效应的表征
  • 批准号:
    2310015
  • 财政年份:
    2023
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Standard Grant
Research in Novel Symmetries of Quantum Field Theory and String Theory
量子场论和弦理论的新对称性研究
  • 批准号:
    2310279
  • 财政年份:
    2023
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Continuing Grant
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:
    $ 40.27万
  • 项目类别:
    Standard Grant
CAREER: Low-energy Nuclear Physics and Fundamental Symmetries with Neutrons and Cryogenic Technologies
职业:低能核物理以及中子和低温技术的基本对称性
  • 批准号:
    2232117
  • 财政年份:
    2023
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Continuing Grant
Random curves and surfaces with conformal symmetries
具有共形对称性的随机曲线和曲面
  • 批准号:
    2246820
  • 财政年份:
    2023
  • 资助金额:
    $ 40.27万
  • 项目类别:
    Continuing Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了