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.
这个项目位于概率、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基础空间对随机过程行为的几何影响,特别是在非光滑几何环境下,包括次黎曼几何。它从概率和分析两方面融合了新的和传统的技术。本项目涉及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。研究项目主要集中在三个主题。第一个主题涉及在Grassman流形和FLAG流形上的几何有意义随机泛函的探索。此外,本主题旨在建立这些泛函和与Berard-Bergery纤维相关的简并扩散过程之间的联系。第二个研究方向围绕次黎曼几何中刚性定理的新方面展开。特别是,该项目旨在研究使用热核的次黎曼模型空间的一种新的分析刻画。本调查将探讨紧凑型和非紧凑型两种情况。第三个主题包括对度量空间中域的等周型问题的概率和分析研究,考虑域的频谱和该域扩散过程的退出时间之间的相互作用。该奖项反映了NSF的法定使命,并通过使用基金会的智力优势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

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会议论文数量(0)
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Jing Wang其他文献

Highly reliable dc SQUIDs in temperature with laser-MBE YBa2Cu3OX thin films
使用激光 MBE YBa2Cu3OX 薄膜在温度下实现高度可靠的直流 SQUID
  • DOI:
    10.1016/s0038-1098(03)00213-8
  • 发表时间:
    2003
  • 期刊:
  • 影响因子:
    2.1
  • 作者:
    Jing Wang;B. Han;F. Chen;T. Zhao;Fengzhi Xu;Yue;G. H. Chen;Hui‐bin Lu;Q. Yang;T. Cui
  • 通讯作者:
    T. Cui
4"-O-Alkylated alpha-Galactosylceramide Analogues as iNKT-Cell Antigens: Synthetic, Biological, and Structural Studies.
4"-O-烷基化 α-半乳糖神经酰胺类似物作为 iNKT 细胞抗原:合成、生物学和结构研究。
  • DOI:
  • 发表时间:
    2019
  • 期刊:
  • 影响因子:
    0
  • 作者:
    J. Janssens;A. Bitra;Jing Wang;T. Decruy;K. Venken;J. V. D. Eycken;D. Elewaut;D. Zajonc;S. V. Calenbergh
  • 通讯作者:
    S. V. Calenbergh
A novel approach for texture shape recovery
一种纹理形状恢复的新方法
Role of platelet infiltration as independent prognostic marker for gastric adenocarcinomas
血小板浸润作为胃腺癌独立预后标志物的作用
Studying the Sent-Down Internet: roundtable on research methods
研究下乡互联网:研究方法圆桌会议
  • DOI:
    10.1080/17544750.2015.991370
  • 发表时间:
    2015
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Elisa Oreglia;J. Qiu;W. Bu;Barbara Schulte;Jing Wang;C. Wallis;Baohua Zhou
  • 通讯作者:
    Baohua Zhou

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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