Conference series in geometric analysis and sub-Riemannian geometry

几何分析和亚黎曼几何会议系列

• 批准号: 0548644
• 负责人: Jeremy Tyson
• 金额: $ 2.7万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-15 至 2007-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0548644&HistoricalAwards=false
• 关键词: Conference; series; geometric; analysis; sub

AbstractAward: DMS-0548644Principal Investigator: Jeremy Tyson, Luca Capogna and Scott PaulsThe conference "Geometric Analysis and Applications" will takeplace at the University of Illinois at Urbana-Champaign in July2006. The focus of the conference will be on recent developmentsin the study of analysis and geometry in metric measure spaceswith a particular emphasis on geometric analysis, geometricmeasure theory and subelliptic PDE in Carnot groups and generalsub-Riemannian manifolds. Applications of these subjects toproblems in robotics, control theory, the geometry of the visualcortex, and digital image reconstruction will also receivesignificant attention. An important aim of the conference is toprovide a forum for the exchange of ideas among researchers in avariety of pure and applied fields and to foster new avenues forcollaboration and exchange.The basic theme of sub-Riemannian geometry is the "geometry ofconstrained motion"; it provides mathematical models for anyphysical situation in which allowable motion is subject tospecific a priori geometric constraints. Historically, the rootsof the subject lie in Carnot's work on thermodynamics andadiabatic processes, but it has progressed significantly beyondthese motivating questions to a central position in modernnonsmooth geometric analysis, and has seen remarkableapplications in numerous areas: robotic path planning, remotecontrol of satellites and unmanned aerial vehicles, digital imagereconstruction and computer vision, neurobiology, and themathematics of finance, to name a few. The goal of the conferenceis to bring together a wide spectrum of pure and appliedmathematicians with common interests in the subject ofsub-Riemannian geometry to develop new methods and techniques forits study. Special emphasis will be placed on supporting graduatestudents and junior participants, to train the next generation ofresearchers in this exciting and rapidly expanding field and tolay the foundation for a "North American" school in this area ona par with the established centers of research in sub-Riemannianand Carnot-Caratheodory geometry in Europe. Further informationregarding the conference can be found atwww.math.uiuc.edu/~tyson/UIUC06.html

AbstractAward：DMS-0548644首席研究员：杰里米泰森，卢卡Capogna和斯科特保罗会议“几何分析和应用”将于2006年7月在伊利诺伊大学厄巴纳香槟分校举行。会议的重点将是最近的发展，在研究分析和几何度量spaceswith特别强调几何分析，geometricmeasure理论和次椭圆偏微分方程在卡诺集团和generalsub-Riemannian流形。这些学科在机器人、控制理论、视觉皮层的几何学和数字图像重建等方面的应用也将受到极大的关注。 会议的一个重要目的是提供一个论坛，为研究人员在各种纯和应用领域的思想交流，并促进新的途径合作和交流。次黎曼几何的基本主题是“几何约束运动”，它提供了数学模型的任何物理情况下，允许的运动是受到特定的先验几何约束。从历史上看，这一主题的根源在于卡诺对热力学和绝热过程的研究，但它已经大大超越了这些激励性问题，成为现代非光滑几何分析的中心位置，并在许多领域得到了广泛的应用：机器人路径规划，卫星和无人驾驶飞行器的远程控制，数字图像重建和计算机视觉，神经生物学和金融数学，仅举几例。会议的目标是汇集广泛的纯数学家和应用数学家的共同利益的主题ofsub-Riemann几何发展新的方法和技术的研究。特别强调将放在支持研究生和初级参与者，培养下一代ofresearchers在这一令人兴奋的和迅速扩大的领域，并奠定了基础，为“北美”学校在这一领域与建立中心的研究在亚黎曼和卡诺-Caratheodory几何在欧洲。有关会议的更多信息，请访问atwww.math.uiuc.edu/~tyson/UIUC06.html