Stochastic processes in sub-Riemannian geometry

亚黎曼几何中的随机过程

基本信息

  • 批准号:
    2246817
  • 负责人:
  • 金额:
    $ 21万
  • 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

项目摘要

This project lies at the intersection of the mathematical areas of probability, analysis and differential geometry. It primarily aims to investigate the geometric influence of the underlying space on the behavior of stochastic processes, particularly in non-smooth geometric settings, including sub-Riemannian geometry. It integrates novel and traditional techniques from probability and analysis. Some problems addressed in this project have relevance to control systems and data science. This project offers collaboration opportunities, as well as mentorship and training for graduate students.The research project primarily focuses on three topics. The first topic involves the exploration of geometrically meaningful stochastic functionals on Grassmannian manifolds and flag manifolds. Additionally, this topic aims to establish connections between these functionals and the degenerate diffusion processes associated with the Berard-Bergery fibration. The second research direction centers around novel aspects of rigidity theorems within sub-Riemannian geometry. In particular, the project aims to investigate a fresh analytical characterization of sub-Riemannian model spaces using heat kernels. Both compact and non-compact cases will be explored in this investigation. The third topic includes both probabilistic and analytic investigation of isoperimetric type problems for domains in metric measure spaces, considering the interplay between the spectrum of a domain and the exit time of a diffusion process from that domain.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.
该项目位于概率,分析和微分几何的数学领域的交叉点。它的主要目的是研究随机过程的行为的基础空间的几何影响,特别是在非光滑的几何设置,包括亚黎曼几何。它集成了概率和分析的新颖和传统技术。该项目中解决的一些问题与控制系统和数据科学有关。该项目为研究生提供合作机会以及指导和培训。该研究项目主要关注三个主题。第一个主题涉及探索几何有意义的随机泛函上的格拉斯曼流形和旗流形。此外,本主题的目的是建立这些泛函和退化扩散过程与Berard-Bergery纤维化之间的联系。第二个研究方向是围绕亚黎曼几何中刚性定理的新方面。特别是,该项目的目的是研究一个新的分析表征亚黎曼模型空间使用热内核。紧和非紧的情况下,将探讨在这项调查。第三个主题包括概率和分析调查的等周型问题的域度量措施spaces.This奖项的频谱域和出口时间的扩散过程从该domain.This奖项之间的相互作用反映了NSF的法定使命,并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

项目成果

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Jing Wang其他文献

The influence of alkali and alkaline earth metal compounds on pyrolysis of peanut shell
碱金属和碱土金属化合物对花生壳热解的影响
  • DOI:
    10.1002/apj.595
  • 发表时间:
    2012-05
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Fen Xin;Jing Wang;Haiping Yang;Xianhua Wang;Hanping Chen
  • 通讯作者:
    Hanping Chen
The determination of patulin from food samples using dual-dummy molecularly imprinted solid-phase extraction coupled with LC-MS/MS.
使用双模拟分子印迹固相萃取结合 LC-MS/MS 测定食品样品中的棒曲霉素。
Distributed traffic regulation and control for multiple autonomous mobile robots operating in discrete space
离散空间中多个自主移动机器人的分布式交通调控
Pore-level numerical analysis of the infrared surface temperature of open-cell metallic foams
开孔金属泡沫红外表面温度的孔级数值分析
Effect of action observation therapy on daily activities and motor recovery in stroke patients
行动观察疗法对脑卒中患者日常活动及运动恢复的影响
  • DOI:
  • 发表时间:
    2015
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Meihong Zhu;Jing Wang;X. Gu;Mei;Ming Zeng;Chunyuan Wang;Qiao;Jian
  • 通讯作者:
    Jian

Jing Wang的其他文献

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{{ truncateString('Jing Wang', 18)}}的其他基金

Collaborative Research: FuSe: Thermal Co-Design for Heterogeneous Integration of Low Loss Electromagnetic and RF Systems (The CHILLERS)
合作研究:FuSe:低损耗电磁和射频系统异构集成的热协同设计(CHILLERS)
  • 批准号:
    2329207
  • 财政年份:
    2023
  • 资助金额:
    $ 21万
  • 项目类别:
    Continuing Grant
Degenerate Diffusions and Related Heat Kernel Estimates
简并扩散和相关的热核估计
  • 批准号:
    1855523
  • 财政年份:
    2019
  • 资助金额:
    $ 21万
  • 项目类别:
    Continuing Grant
MRI: Acquisition of a Multi-Material Additive Manufacturing Platform for Multi-Disciplinary Research and Education
MRI:收购用于多学科研究和教育的多材料增材制造平台
  • 批准号:
    1726875
  • 财政年份:
    2017
  • 资助金额:
    $ 21万
  • 项目类别:
    Standard Grant
I-Corps Teams: Pathways to Market of Piezoelectric Elastomer Composites for Additive Manufacturing of Flexible 3D Conformal Acoustic Emission and Ultrasonic Transducer Arrays
I-Corps 团队:用于柔性 3D 共形声发射和超声波换能器阵列增材制造的压电弹性体复合材料的市场之路
  • 批准号:
    1606755
  • 财政年份:
    2015
  • 资助金额:
    $ 21万
  • 项目类别:
    Standard Grant
Spline-based Empirical Likelihood and Qausi-likelihood Estimation
基于样条的经验似然和 Qausi 似然估计
  • 批准号:
    1107017
  • 财政年份:
    2011
  • 资助金额:
    $ 21万
  • 项目类别:
    Standard Grant
GOALI/Collaborative Research: Antenna-Coupled ALD-Enabled Metal-Insulator-Insulator-Metal Diodes for High Responsivity and High Resolution THz/Infrared Focal Plane Arrays
GOALI/合作研究:用于高响应度和高分辨率太赫兹/红外焦平面阵列的天线耦合 ALD 金属-绝缘体-绝缘体-金属二极管
  • 批准号:
    1029067
  • 财政年份:
    2010
  • 资助金额:
    $ 21万
  • 项目类别:
    Continuing Grant
Imprinting learning in Drosophila
果蝇的印记学习
  • 批准号:
    0920668
  • 财政年份:
    2009
  • 资助金额:
    $ 21万
  • 项目类别:
    Standard Grant
GOALI/Collaborative Research: Passive, Diamagnetic Inertial Sensing Integrated with High-Sensitivity Telemetry
GOALI/合作研究:无源抗磁惯性传感与高灵敏度遥测集成
  • 批准号:
    0925929
  • 财政年份:
    2009
  • 资助金额:
    $ 21万
  • 项目类别:
    Standard Grant

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Submesoscale Processes Associated with Oceanic Eddies
  • 批准号:
  • 批准年份:
    2022
  • 资助金额:
    160 万元
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