RUI: Pure and Applied Knot Theory: Skeins, Hyperbolic Volumes, and Biopolymers
RUI:纯结理论和应用结理论:绞纱、双曲体积和生物聚合物
基本信息
- 批准号:2305414
- 负责人:
- 金额:$ 28.14万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2023
- 资助国家:美国
- 起止时间:2023-07-15 至 2026-06-30
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
Knot theory is the mathematical study of entanglement of loops up to continuous deformation. One can create a knot by taking an entangled string and connecting the endpoints, and two knots are equivalent if one can continuously deform one to the other, for example by bending, stretching, and passing strands inside and through others, but without cutting or breaking the string in any way. This project considers both theoretical problems and applications of mathematical knot theory. One group of problems studies a family of invariants of knots related to quantum field theory from physics. More specifically, the project seeks to understand how the quantum invariant of a knot detects geometric properties of the knot and the 3-dimensional spaces that can be associated with it. The mathematical techniques from this research has potential applications to mathematical physics and theoretical topological quantum computing. Another group of problems concerns applications to the study of knotted proteins and other biopolymers, some of which are known to be associated to various diseases. The project uses knot theory techniques to develop a model that can be used to quantify and to relate local topological complexity with biophysical processes. The model can also be used to potentially design synthetic biopolymers with special biophysical properties. The project includes a number of research problems suitable for collaboration with undergraduate students, as well as outreach and dissemination activities that seek to increase interest in mathematics more generally. The PI has successfully involved undergraduate students in similar research in the past and will continue to advise and encourage students to continue careers in mathematics and related areas. The research is split into three parts, two seek to connect quantum topology with hyperbolic geometry and one applies knot theory to molecular biology. One project concerns a version of the Volume Conjecture based the theory of the Kauffman bracket skein algebra from quantum topology and its relationship to the Teichmuller space of a surface from hyperbolic geometry. A second project studies algebraic and geometric properties of a generalization of the Kauffman bracket algebra which is related to the decorated Teichmuller space of a surface with punctures. A third project involves a collaboration with a biophysicist to study local entanglements that are held tightly in place by molecular forces in biopolymers. The proposed knot-theoretic model would give a description of such local entanglements, allowing one to quantify and measure changes in the local topological complexity of biopolymers in experiments.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.
结理论是循环纠缠到连续变形的数学研究。一个人可以通过取一个纠缠的绳子并连接端点来创建一个结,如果一个结可以连续变形,例如,两个结是等效的,例如,通过弯曲,伸展和通过其他链条将链弯曲,伸展和通过其他链,而不以任何方式切割或破坏字符串。 该项目考虑了数学结理论的理论问题和应用。一组问题研究了与物理学的量子场理论有关的一系列不变的结。更具体地说,该项目试图了解结的量子不变性如何检测结的几何特性以及可以与之相关的3维空间。这项研究的数学技术在数学物理学和理论拓扑量子计算上具有潜在的应用。另一组问题涉及对打结蛋白和其他生物聚合物的研究的应用,其中一些与各种疾病有关。该项目使用结理论技术来开发一个可用于量化和将局部拓扑复杂性与生物物理过程相关联的模型。该模型还可以用于设计具有特殊生物物理特性的合成生物聚合物。该项目包括许多适用于与本科生合作的研究问题,以及寻求更普遍地增加对数学兴趣的外展和传播活动。 PI过去曾成功与本科生一起参与了类似的研究,并将继续为学生提供数学和相关领域的职业提供建议和鼓励。 这项研究分为三个部分,两部分试图将量子拓扑与双曲线几何形状联系起来,而一部分将结理论应用于分子生物学。一个项目涉及量子拓扑的Kauffman支架绞线代数的理论,涉及量子拓扑及其与双曲线几何形状与表面的Teichmuller空间的关系。第二个项目研究Kauffman支架代数的代数和几何特性,该代数与带有穿刺的表面装饰的Teichmuller空间有关。第三个项目涉及与生物物理学家的合作研究,以研究由生物聚合物中的分子力紧紧地固定在适当位置的局部纠缠。所提出的结论模型将描述此类本地纠缠,使人们可以在实验中量化和衡量生物聚合物局部拓扑复杂性的变化。该奖项反映了NSF的法定任务,并被认为是值得通过基金会的知识分子优点和更广泛影响的审查标准来通过评估来通过评估来支持的。
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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Helen Wong其他文献
Sa342 FAST SCORE REAL LIFE EXPERIENCE: IMPLICATIONS FOR CLINICAL PRACTICE
- DOI:
10.1016/s0016-5085(21)02701-3 - 发表时间:
2021-05-01 - 期刊:
- 影响因子:
- 作者:
Kartheek Dasari;Minh Trannguyen;Thimmaiah Theethira;Helen Wong;Marina Roytman - 通讯作者:
Marina Roytman
The Delivery of Palliative and End-of-Life Care to Adolescents and Young Adults Living with Cancer: A Scoping Review.
向患有癌症的青少年和年轻人提供姑息治疗和临终关怀:范围界定审查。
- DOI:
10.1089/jayao.2023.0013 - 发表时间:
2023 - 期刊:
- 影响因子:2
- 作者:
E. Drake;Lori E Weeks;Michael van Manen;H. Shin;Helen Wong;Dani Taylor;Shelley McKibbon;Janet Curran - 通讯作者:
Janet Curran
Salvage surgery for local regrowth following external beam radiotherapy followed by contact X-ray brachytherapy and 'watch & wait' for rectal cancer. Do we compromise the chance of cure?
- DOI:
10.1016/j.ejso.2018.01.543 - 发表时间:
2018-03-01 - 期刊:
- 影响因子:
- 作者:
Arthur Sun Myint;Fraser Smith;Helen Wong;Karen Whitmarsh;Raj Sripadam;Chris Rao;Kate Perkins;Mark Pritchard - 通讯作者:
Mark Pritchard
High Performance Silicon Nitride Passive Optical Components on Monolithic Silicon Photonics Platform
单片硅光子平台上的高性能氮化硅无源光学元件
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
S. Chandran;Yusheng Bian;Won Suk Lee;Ahmed Abumazwed;Neng Liu;Luhua Xu;Hanyi Ding;A. Aboketaf;Michal Rakowski;K. Dezfulian;Arman Najafi;T. Hirokawa;Qidi Liu;A. Stricker;S. Krishnamurthy;K. McLean;R. Sporer;Michelle Zhang;Shenghua Song;Helen Wong;Salman Mosleh;D. Deptuck;Janet Tinkler;Jae Gon Lee;Vikas Gupta;A. Yu;K. Giewont;T. Letavic - 通讯作者:
T. Letavic
Salvage surgery for local regrowth following external beam radiotherapy followed by contact X-ray brachytherapy and ‘Watch & wait’ for rectal cancer. Do we compromise the chance of cure?
- DOI:
10.1016/j.ejso.2017.10.145 - 发表时间:
2017-11-01 - 期刊:
- 影响因子:
- 作者:
Arthur Sun Myint;Fraser Smith;Helen Wong;Karen Whitmarsh;Raj Sripadam;Chris Rao;Kate Perkins;Mark Pritchard - 通讯作者:
Mark Pritchard
Helen Wong的其他文献
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{{ truncateString('Helen Wong', 18)}}的其他基金
RUI: Knots in Three-Dimensional Manifolds: Quantum Topology, Hyperbolic Geometry, and Applications
RUI:三维流形中的结:量子拓扑、双曲几何和应用
- 批准号:
1906323 - 财政年份:2019
- 资助金额:
$ 28.14万 - 项目类别:
Standard Grant
RUI: Relating quantum and classical topology and geometry
RUI:关联量子和经典拓扑和几何
- 批准号:
1105692 - 财政年份:2011
- 资助金额:
$ 28.14万 - 项目类别:
Standard Grant
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