Geometric, Optimizational and Spectral Problems in Large Random Structures
大型随机结构中的几何、优化和谱问题
基本信息
- 批准号:1953848
- 负责人:
- 金额:$ 37.53万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2020
- 资助国家:美国
- 起止时间:2020-09-01 至 2024-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The research supported by this award focuses on large random structures that have strong motivation from a number of physical disciplines. The PI attempts to improve understanding on a range of fundamental models and phenomena in mathematical physics and computer science, including the insulator-conductor transition, the limit of computing power in solving realistic problems, and some two-dimensional random surface models of importance to conformal field theory. In addition, the PI is actively collaborating on application-oriented projects, and one of the specific goals is to help consolidating theoretical foundations for some statistical learning procedures. Finally, the PI intends to provide research opportunities for graduate students and postdoctoral researchers in probability theory.The PI will study limiting behavior for stochastic models with emphasis on geometric, optimizational and spectral aspects as well as interactions among them. The stochastic processes under consideration cover a wide range of spectrum and are of fundamental importance in respective research communities. For instance, random geometry of Gaussian free field has been a phenomenal research topic in two-dimensional probability, and the closely related Liouville quantum gravity surfaces can be thought of as the canonical models of random two-dimensional Riemannian manifolds; random constraint satisfaction problems have strong connections with spin glass theory and complexity theory, and it is of major interest to understand the connections between the phase transitions of the solution spaces and the algorithmic transitions; random field model has been a classic example in understanding how presence of disorder affects the behavior of statistical physics models; Anderson localization for random Schroedinger operators is motivated by understanding the conductor-insulator transition. In order to make progress on these problems, the PI will attempt to bring in new insights from physics, develop new mathematical tools and identify new connections among different mathematical branches.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.
该奖项支持的研究重点是大型随机结构,这些结构具有来自许多物理学科的强烈动机。PI试图提高对数学物理和计算机科学中一系列基本模型和现象的理解,包括绝缘体-导体过渡,解决现实问题的计算能力极限,以及一些对共形场论重要的二维随机表面模型。此外,PI正在积极合作开展面向应用的项目,具体目标之一是帮助巩固一些统计学习程序的理论基础。最后,PI旨在为概率论的研究生和博士后研究人员提供研究机会。PI将研究随机模型的极限行为,重点是几何,优化和谱方面以及它们之间的相互作用。所考虑的随机过程涵盖了广泛的频谱,并在各自的研究社区具有根本的重要性。例如,高斯自由场的随机几何已经成为二维概率论中的一个现象学研究课题,与之密切相关的Liouville量子引力曲面可以看作是随机二维黎曼流形的正则模型;随机约束满足问题与自旋玻璃理论和复杂性理论有很强的联系,理解解空间的相变和算法转换之间的联系是主要的兴趣;随机场模型是理解无序的存在如何影响统计物理模型行为的经典例子;随机薛定谔算符的安德森定域化是由对导体-绝缘体相变的理解所激发的。为了在这些问题上取得进展,PI将尝试从物理学中引入新的见解,开发新的数学工具,并确定不同数学分支之间的新联系。该奖项反映了NSF的法定使命,并通过使用基金会的智力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(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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Jian Ding其他文献
Topoisomerase II inhibitors from the roots of Stellera chamaejasme L.
来自狼毒根的拓扑异构酶 II 抑制剂。
- DOI:
10.1016/j.bmc.2014.05.042 - 发表时间:
2014-08 - 期刊:
- 影响因子:0
- 作者:
Ting Peng;Hua Xie;Jian Ding;Hong-Bing Wang - 通讯作者:
Hong-Bing Wang
Thermally treated soya bean oleosomes: the changes in their stability and associated proteins
热处理大豆油质体:其稳定性和相关蛋白质的变化
- DOI:
10.1111/ijfs.14266 - 发表时间:
2019 - 期刊:
- 影响因子:3.3
- 作者:
Jian Ding;Zejian Xu;Baokun Qi;Zongzhong Liu;Liangli Yu;Zhang Yan;Lianzhou Jiang;Xiaonan Sui - 通讯作者:
Xiaonan Sui
Kinetic and thermodynamic aspects of arsenate adsorption on aluminumoxide modi?ed palygorskite nanocomposites
氧化铝改性凹凸棒石纳米复合材料上砷酸盐吸附的动力学和热力学方面
- DOI:
- 发表时间:
2013 - 期刊:
- 影响因子:15.1
- 作者:
Jingyuan Wang;Yue Chang;Jian Ding;Jian Ma - 通讯作者:
Jian Ma
Multifaceted effects of astragaloside IV on promotion of random pattern skin flap survival in rats
黄芪甲苷IV对促进大鼠随机皮瓣存活的多方面作用
- DOI:
- 发表时间:
2017 - 期刊:
- 影响因子:0
- 作者:
Renjin Lin;Huanwen Chen;Daniel Callow;Shihen Li;Lei Wang;Shi Li;Long Chen;Jian Ding;Weiyang Gao;Huazi Xu;Jianzhong Kong;Kailiang Zhou - 通讯作者:
Kailiang Zhou
Relationship Between Blood Fibrinogen Concentration and Pathological Features of Cancer Patients: A 139-case Clinical Study
癌症患者血纤维蛋白原浓度与病理特征关系:139例临床研究
- DOI:
10.3844/ojbsci.2007.8.11 - 发表时间:
2007 - 期刊:
- 影响因子:0
- 作者:
D. Lu;Xuelian Chen;Min Huang;Bin Xu;Jian Ding - 通讯作者:
Jian Ding
Jian Ding的其他文献
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{{ truncateString('Jian Ding', 18)}}的其他基金
CAREER: Stochastic processes in statistical physics and optimization
职业:统计物理和优化中的随机过程
- 批准号:
1757479 - 财政年份:2017
- 资助金额:
$ 37.53万 - 项目类别:
Continuing Grant
CAREER: Stochastic processes in statistical physics and optimization
职业:统计物理和优化中的随机过程
- 批准号:
1455049 - 财政年份:2015
- 资助金额:
$ 37.53万 - 项目类别:
Continuing Grant
Extreme Values For Random Processes of Tree Structure
树结构随机过程的极值
- 批准号:
1207988 - 财政年份:2012
- 资助金额:
$ 37.53万 - 项目类别:
Standard Grant
Extreme Values For Random Processes of Tree Structure
树结构随机过程的极值
- 批准号:
1313596 - 财政年份:2012
- 资助金额:
$ 37.53万 - 项目类别:
Standard Grant